The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in $AdS_{4}$ space is analyzed in details. Possible interactions with the Higgs scalar and the corresponding one loop mass renormalization are studied. This mass renormalization is finite and connected with the anomalous dimensions of those currents in the corresponding boundary $CFT_{3}$ that cease to be conserved when the interaction is switched on. In particular it is proportional to $\ell-2$.
We revisit our recently proposed formalism for dealing with the heavy quark limit of the quark Dyson-Schwinger equation. An ambiguity inherent in the original version of method is identified and resolved. Our reanalysis illustrates the importance of correctly accounting for the effect of hard gluon momenta on the heavy quark self energy in the vicinity of the bare fermion mass pole.
We discuss the dynamical situation which arises in a local quantum field theory after renormalization. By using the example of the three-dimensional theory of a neutral scalar field interacting through the quartic coupling, we show that after renormalization the dynamics of a theory is governed by a generalized dynamical equation with a nonlocal interaction operator. It is shown that the generalized dynamical equation allows one to formulate this theory in an ultraviolet-finite way.
We study the ultraviolet properties of theories whose fundamental fields display a confining, Gribov-type, propagator. These are propagators that exhibit complex poles and violate positivity, thus precluding a physical propagating particle interpretation. We show that the properties of this type of confining propagators do not change the ultraviolet behavior of the theory, in the sense that no new ultraviolet primitive divergences are generated, thus securing the renormalizability of these confining theories. We illustrate these properties by studying a variety of models, including bosonic and…
The recent investigations of pure Landau gauge SU(3) Yang-Mills theories which are based on the truncated Schwinger-Dyson equations (SDE) indicate an infrared power law behavior of the gluon and the ghost propagators. It has been shown that the gluon propagator vanishes (or finite) in the infrared limit, while the ghost propagator is more singular than a massless pole, and also that there exists an infrared fixed point of the running gauge coupling. In this paper we reexamine this picture by means of the exact (non-perturbative) renormalization group (ERG) equations under some approximation sc…
We examine the possibility that there may exist a logarithmic correction to the infrared asymptotic solution with power behavior which has recently been found for the gluon and Faddeev-Popov ghost propagators in the Landau gauge. We propose a new Ansatz to find a pair of solutions for the gluon and ghost form factors by solving the coupled Schwinger-Dyson equation under a simple truncation. This Ansatz enables us to derive the infrared and ultraviolet asymptotic solutions simultaneously and to understand why the power solution and the logarithmic solution is possible only in the infrared and u…
I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary space-time dimensions. I prove that when the space-time manifold admits a metric of constant curvature the propagator is not affected by terms with higher derivatives. More generally, certain lagrangian terms are not turned on by renormalization, if they are absent at the tree level. This restricts the form of the action of a non-renormalizable theory, and has applications to quantum gravity. The new action contains infinitely many couplings, but not all of the ones that might have…
We study the analytic structure of the resummed graviton propagator, inspired by the possible existence of black hole precursors in its spectrum. We find an infinite number of poles with positive mass, but both positive and negative effective width, and studied their asymptotic behaviour in the infinite sheet Riemann surface. We find that the stability of these precursors depend crucially on the value of the normalisation point scale.
The study of renormalization of Yang-Mills fields in the light-front gauge has always been a delicate subject in that divergent {\em non-local} terms arise from the calculations of Feynman diagrams. In this short paper we show that this happened because of a deficiency in the gauge fixing procedure that results in an incorrect propagator and propose a cure for it by considering the {\em correct} propagator for the gauge potential. We explicitly show that the use of our correct propagator in the light-front leads to a vacuum polarization tensor at the one-loop level that is free of non-local te…
We study Landau-gauge Yang-Mills theory by means of a nonperturbative vertex expansion of the quantum effective action. Using an exact renormalization group equation, we compute the fully dressed gluon and ghost propagators to lowest nontrivial order in the vertex expansion. In the mid-momentum regime, $p^2\sim\mathcal{O}(1)\text{GeV}^2$, we probe the propagator flow with various {\em ansätze} for the three- and four-point correlations. We analyze the potential of these truncation schemes to generate a nonperturbative scale. We find universal infrared behavior of the propagators, if the gluon …
We reexamine the conventional arguments concerned with the scaling and decoupling solutions for the ghost and gluon propagators in the Landau gauge Yang-Mills theory. We point out a few issues to be clarified, which seems to be overlooked in the previous investigations in this field, in the fully non-perturbative treatment. We propose a trick which enables one to incorporate the Gribov horizon directly into the self-consistent Schwinger-Dyson equation in the gauge-fixed Yang-Mills theory, using the Gribov-Zwanziger framework with the horizon term. We obtain the following results, irrespective …
The infrared behavior of gluon and ghost propagators in Landau gauge Yang-Mills theory has been at the center of an intense debate over the last decade. Different solutions of the Dyson-Schwinger equations show a different behavior of the propagators in the infrared: in the so-called scaling solutions both propagators follow a power law, while in the decoupling solutions the gluon propagator shows a massive behavior. The latest lattice results favor the decoupling solutions. In this contribution, after giving a brief overview of the present status of analytical and semi-analytical approaches t…
The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the noncovariant light-cone gauge (lcg). (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n^*-prescription for the spurious poles of 1/qn, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma_2 contains both covariant and …
We discuss the cyclic Wilson loop, i.e. a rectangular Wilson loop that spans the entire compactified time axis in the imaginary time formalism. The result of a perturbative calculation at $O(α_s^2)$ is given, with the main focus on the ultraviolet divergences of this operator. Based on a general analysis of divergences in loop diagrams, we find that, unlike usual Wilson loops, the cyclic loop does not have cusp divergences but intersection divergences, where the intersections arise due to the periodic boundary conditions. As a result, the cyclic Wilson loop itself is not multiplicatively renor…
Using differential renormalization, we calculate the complete two-point function of the background gauge superfield in pure N=1 Supersymmetric Yang-Mills theory to two loops. Ultraviolet and (off-shell) infrared divergences are renormalized in position and momentum space respectively. This allows us to reobtain the beta function from the dependence on the ultraviolet renormalization scale in an infrared-safe way. The two-loop coefficient of the beta function is generated by the one-loop ultraviolet renormalization of the quantum gauge field via nonlocal terms which are infrared divergent on sh…
We calculate the ultraviolet divergences in a weak field expansion of the Volkov propagator. This is done for the full Lorentz class of gauges. The expected gauge invariance of the vacuum mass shift in each sideband is recovered. However, the renormalisation of the background induced mass shift is shown to be gauge dependent. In particular, we show that it vanishes in Landau gauge. We find that only in that gauge does the vacuum renormalisation remove all ultraviolet divergences.
With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic struc…
The Planck length is the minimum length which physical law do not fail. The Dirac delta function was created to deal with continuous range issue, and it is zero except for one point. Thus contradict the Planck length. Renormalization method is the usual way to deal with divergence difficulties. The authors proposed a new way to solve the problem of ultraviolet divergence and this method is self-consistent with the Planck length. For this purpose a redefine function $δ_P$ in position representation was introduced to handle with the canonical quantization. The function $δ_P$ tends to the Dirac d…
Within the refined Gribov-Zwanziger scenario for four-dimensional Yang-Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that simply adding a gluon mass term to the usual Faddeev-Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in good agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization…
We point out that perturbation theory in conjunction with the renormalization group (RG) puts a severe constraint on the structure of the large-N non-perturbative glueball propagators in SU(N) pure YM, in QCD and in n=1 SUSY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure YM and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al.…
The interpretation of the Landau gauge lattice gluon propagator as a massive type bosonic propagator is investigated. Three different scenarios are discussed: i) an infrared constant gluon mass; ii) an ultraviolet constant gluon mass; iii) a momentum dependent mass. We find that the infrared data can be associated with a massive propagator up to momenta $\sim 500$ MeV, with a constant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis, or 648(7) MeV, if the zero momentum gluon propagator is included in the data sets. The ultraviolet lattice data is …
The two--dimensional topological BF model is considered in the Landau gauge in the framework of perturbation theory. Due to the singular behaviour of the ghost propagator at long distances, a mass term to the ghost fields is introduced as infrared regulator. Relying on the supersymmetric algebraic structure of the resulting massive theory, we study the infrared and ultraviolet renormalizability of the model, with the outcome that it is perturbatively finite.
We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-H…
We discuss renormalization of propagator of interacting Rarita--Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For non-leading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of $Δ^{++}(1232)$ in $π^{+}\particle{p}\to π^{+}\particle{p}$ leads to good description of total cross-section and to reasonable agreement with results of…
We consider the real-time holography on Anti-de-Sitter (AdS) and more generally on Lifshitz spacetimes for spinorial fields. The equation of motion for fermions on general Lifshitz space is derived. Analytically solvable cases are identified. On AdS space we derived time-ordered, time-reversed, advanced and retarded propagators with the correct i ε-insertions. Using the Keldysh-Schwinger contour we also calculated a propagator on thermal AdS. For massless fermions on the Lifshitz spacetime with z=2 we calculated the Euclidean 2-point function and explored the structure of divergences of the on…
A short outline is given on the application of differential regularization to QCD in the background-field method. The derivation of the propagators in the background gluon field as short-distance expansions is described and the renormalization of the theory is mentioned.
We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions and their expansions through two loops for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormali…
The well-known physical equivalence drawn from hole theory is applied in this article. The author suggests to replace, in the part of Feynman diagram which cannot be fixed by experiments, each fermion field operator, and hence fermion propagator, by pairs of equivalent fermion field operators and propagators. The formulation of this article thus yields additional terms which reveal characteristic effects that have not been explored previously; such characteristic effects lead to the appearence of logarithmic running terms and that finite radiative corrections are directly obtained in calculati…
The properties of strongly gravitating systems suggest that field theory overcounts the states of a system. Reducing the number of degrees of freedom, without abandoning the notion of effective field theory, may be achieved through a connection between the ultraviolet and infrared cutoffs. We provide an implementation of this idea within the Wilsonian approach to the renormalization group. We derive an exact flow equation that describes the evolution of the effective action. We discuss the implications for the existence of infrared fixed points and the running of couplings. We also give an alt…
We calculate the change in the ultraviolet behaviour of the vortex operator due to the presence of dynamical Higgs field in both 2+1 dimensional QED and the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the presence of the Higgs field leads at the one loop level to power like correction to the propagator of the vortex operator. On the other hand, in the Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex propagator. Thus, as long as the mass of the Higgs field is much larger than the gauge coupling constant, the ultraviolet behaviour of the vort…
Structure of quantum corrections in ${\cal N}=1$ supersymmetric gauge theories is investigated in the case of using the regularization by higher covariant derivatives. It is demonstrated that this regularization allows revealing some interesting features which lead to the exact relations between the renormalization group functions. In particular, the NSVZ equation, which relates the $β$-function to the anomalous dimension of the matter superfields, naturally appears in this case. We briefly review the all-loop derivation of this equation and the construction of a simple renormalization prescri…
We extend the recent one loop analysis of the ultraviolet completion of the $CP(N)$ nonlinear $σ$ model in six dimensions to two loop order in the MSbar scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and $β$-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a non-trivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson-Fisher fixed …
This paper proposes a different interpretation on the renormalization program of an interacting Klein-Gordon field in curved space-times. Rather than being just another renormalization program we argue that it that it makes the QFT ultraviolet-finite at its foundation. More precisely, we argue that renormalization is a part of the foundation of QFT and that without it the theory is mathematically ill-defined or at the very least incompletely specified.
The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index-spinor formulation within the BFV-BRST approach. None renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index-free form with the use of index spinor. The choice of boundary conditions on the index spinor determines holomorphic or antiholomorphic representation for the canonical description of particle/antiparticle spin.
We reassess the problem of renormalization in finite temperature field theory (FTFT). A new point of view elucidates the relation between the ultraviolet divergences for T=0 and $T \not= 0$ theories and makes clear the reason why the ultraviolet behavior keeps unaffected when we consider the FTFT version associated to a given quantum field theory (QFT). The strength of the derivation one lies on the Hörmander's criterion for the existence of products of distributions in terms of the wavefront sets of the respective distributions. The approach allows us to regard the FTFT both imaginary and rea…
We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function $A(p^2)$ in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential which will be a useful means to research c…
We prove an asymptotic structure theorem for glueball and meson propagators of any spin in large-N QCD and in n=1 SUSY QCD with massless quarks, that determines asymptotically the residues of the poles of the propagators in terms of their anomalous dimensions and of the spectral density of the masses. The asymptotic theorem follows by the severe constraints on the propagators in large-N QCD with massless quarks, or in any large-N confining asymptotically-free gauge theory massless in perturbation theory, that arise by perturbation theory in conjunction with the renormalization group and by the…
The full gluon propagator relevant for the description of the truly non-perturbative QCD dynamics, the so-called intrinsically non-perturbative gluon propagator has been derived in our previous work. It explicitly depends on the regularized mass gap, which dominates its structure at small gluon momentum. It is automatically transversal in a gauge invariant way. It is characterized by the presence of severe infrared singularities at small gluon momentum, so the gluons remain massless, and this does not depend on the gauge choice. In this paper we have shown how precisely the renormalization pro…
The renormalization procedure for the Yang-Mills theory in the gauge free of the Gribov ambiguity is constructed. It is shown that all the ultraviolet infinities may be removed by renormalization of the parameters entering the classical Lagrangian and the local redefinition of the fields.
In our previously published papers, it was proved that the chromodynamics with massive gluons can well be set up on the gauge-invariance principle. The quantization of the chromodynamics was perfectly performed in the both of Hamiltonian and Lagrangian path-integral formalisms by using the Lagrangian undetermined multiplier method. In this paper, It is shown that the quantum theory is invariant with respect to a kind of BRST-transformations. From the BRST-invariance of the theory, the Ward-Takahashi identities satisfied by the generating functionals of full Green functions, connected Green fun…
We construct the massive scalar propagator for planar gravitational wave backgrounds propagating on Minkowski space. We represent the propagator in terms of the Bessel's function of suitably deformed nonlocal distance functions, the deformation being caused by gravitational waves. We calculate the propagator both for nonpolarized, for the plus ($+$) and cross ($\times$) polarized plane waves, as well as for more general planar waves both in $D$ space-time dimensions. The propagator is useful for studying interactions of scalar fields on planar gravitational wave backgrounds in the context of i…
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the harmonic oscillator as inputs. We obtain closed form results in the infrared and ultraviolet regimes that give Lorentz invariance violating dispersion relations, and show suppression of propagation at sufficiently high energy.
We perform a calculation of the full momentum dependence of the gluon and ghost propagators in pure SU(3) Yang-Mills theory by integrating Wilson's exact renormalization group equations with respect to an infrared cutoff k. The heavy quark potential in the quenched approximation can be expressed in terms of these propagators. Our results strongly indicate a 1/p^4 behaviour of the heavy quark potential for $p^2 \to 0$. We show in general, that effective actions which satisfy Schwinger-Dyson equations, correspond to (quasi-) fixed points of Wilson's exact renormalization group equations.
Gluon, ghost, and quark propagators are computed in the Schwinger-Dyson formalism. The full set of one-loop and two-loop contributions to the gap equations are evaluated for the first time. A new and efficient method for dealing with quadratic divergences is presented and a consistent renormalization method is proposed. We find that the two-loop contribution to the propagators is subleading, good fits to lattice data are possible, and reliable vertex models are important to obtaining desired ultraviolet, infrared, and gauge-symmetric behavior.
The perturbative description of an electron propagating in a plane wave background is developed and loop corrections analysed. The ultraviolet divergences and associated renormalisation are studied using the sideband framework within which the multiplicative form of the corrections becomes manifest. An additional renormalisation beyond that usually expected is identified and interpreted as a loop correction to the background induced mass term. Results for the strong field sector are conjectured.
We propose to include gravity in quantum field theory non-perturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space-time determined by the four-momenta of the other particles in the same graph. By making additional working assumptions, we are able to put this idea at work in a simplified context, and obtain a modified Feynman propagator for the massless neutral scalar field. Our expression shows a suppression at high momentum, strong enough to entail finite results, to all loop orders, for processes involving at least two virtual particles.
I introduce an approximation scheme that allows to deduce differential equations for the renormalization group $β$-function from a Schwinger--Dyson equation for the propagator. This approximation is proven to give the dominant asymptotic behavior of the perturbative solution. In the supersymmetric Wess--Zumino model and a $ϕ^3_6$ scalar model which do not have divergent vertex functions, this simple Schwinger--Dyson equation for the propagator captures the main quantum corrections.
We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to Ostrogradski ghosts which signal an instability of the system and are therefore dangerous for the consistency of the theory. Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety. Our work then establishes the fol…
We reformulate the coupled set of continuum equations for the renormalized gluon and ghost propagators in QCD, such that the multiplicative renormalizability of the solutions is manifest, independently of the specific form of full vertices and renormalization constants. In the Landau gauge, the equations are free of renormalization constants, and the renormalization point dependence enters only through the renormalized coupling and the renormalized propagator functions. The structure of the equations enables us to devise novel truncations with solutions that are multiplicatively renormalizable…
We revisit the unparticle interactions and propagators from the AdS-CFT point of view, and we show how the contact terms and their renormalization group flow appear in the context of the holographic renormalization. We study both vector unparticles and unfermions, uncovering the relevant boundary conditions and renormalization group flows.
According to the asymptotic-safety conjecture, the gravitational renormalization group flow features an ultraviolet-attractive fixed point that makes the theory renormalizable and ultraviolet complete. The existence of this fixed point entails an antiscreening of the gravitational interaction at short distances. In this paper we review the state-of-the-art of phenomenology of Asymptotically Safe Gravity, focusing on the implications of the gravitational antiscreening in cosmology.
We derive general properties of the scale-dependent effective spectral dimensions of non-perturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short time scales the anomalous dimensions of the propagators lead to a slight decrease of the spectral dimension as compared to the one of a free propagator. Lowering the momentum scale, the spectral dimension decreases further. The class of propagators which display a maximum at Euclidean momenta, and thus violate positivity, always approaches a spectral dimension of …
The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. General expressions for the unrenormalized and renormalized dressed propagators of unstable fermions and their field-renormalization constants are presented.
Resembling the renormalization group from ultraviolet to infrared, we construct a dynamical holographic model in the graviton-dilaton-scalar framework, where the dilaton background field $Φ$ and scalar field $X$ are responsible for the gluodynamics and chiral dynamics, respectively. At the UV boundary, the dilaton field is dual to the dimension-4 gluon operator, and the scalar field is dual to the dimension-3 quark-antiquark operator. The metric structure at IR is automatically deformed by the nonperturbative gluon condensation and chiral condensation in the vacuum. The produced scalar gluebal…
We have formulated new quantum model of the QCD vacuum using the effective potential approach for composite operators. It is based on the existence and importance of such kind of the nonperturbative, topologically nontrivial excitations of gluon field configurations, which can be effectively correctly described by the $q^{-4}$-type behavior of the full gluon propagator in the deep infrared domain. The ultraviolet part of the full gluon propagator was approximated by the asymptotic freedom to-leading order perturbative logarithm term of the running coupling constant. Despite the vacuum energy d…
We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this prop…
In this paper we provide exact expressions for propagators of noncommutative Bosonic or Fermionic field theories after adding terms of the Grosse-Wulkenhaar type in order to ensure Langmann-Szabo covariance. We emphasize the new Fermionic case and we give in particular all necessary bounds for the multiscale analysis and renormalization of the noncommutative Gross-Neveu model.
We extend the ${\cal O}(α_s^5)$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.
We present a relation which connects the propagator in the radial (Fock-Schwinger) gauge with a gauge invariant Wilson loop. It is closely related to the well-known field strength formula and can be used to calculate the radial gauge propagator. The result is shown to diverge in four-dimensional space even for free fields, its singular nature is however naturally explained using the renormalization properties of Wilson loops with cusps and self-intersections. Using this observation we provide a consistent regularization scheme to facilitate loop calculations. Finally we compare our results wit…
We study renormalization of Coulomb-gauge QCD within the Lagrangian second-order formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analyses, we show that, in the strict Coulomb gauge, g^2D^{00} is invariant under renormalization. (D^{00} is the time-time component of the gluon propagator.)
