Although gauge-boson propagators in asymptotically-free gauge theories satisfy a dispersion relation, they do not satisfy the Källen-Lehmann (KL) representation because the spectral function changes sign. We argue that this is a simple consequence of asymptotic freedom. On the basis of the QED-like Ward identities of the pinch technique (PT) we claim that the product of the coupling $g^2$ and the scalar part $\hat{d}(q^2)$ of the PT propagator, which is both gauge invariant and renormalization-group invariant, can be factored into the product of the running charge $\bar{g}^2(q^2)$ and a term $\hat{H}(q^2)$ both of which satisfy the KL representation although their product does not. We show that this behavior is consistent with some simple analytic models that mimic the gauge-invariant PT Schwinger-Dyson equations (SDE) provided that the dynamic gauge boson mass is sufficiently large. The PT SDEs do not depend directly on the PT propagator through $\hat{D}$ but only through $\hat{H}$.
The operator-product expansion(OPE) could be employed to obtain the lowest-order, nonlocal quark scalar condensate component of gluon vacuum polarization. In particular, nonlocal quark scalar condensate can be calculated by solving Dyson-Schwinger Equation(DSE) of QCD. Then, field-theoretic aspects of the gluon vacuum polarization and nonperturbative gluon propagator will be considered in the Landau gauge of the Lorentz gauge fixing. The gluon propagator we obtained is finite in the infrared domain where the single gluon mass $m_g$ can be determined. Our results of the ratio $m_{g}/Λ_{QCD}$ th…
Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles.The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is …
We consider the extension of techniques for bounding higher-dimension operators in quantum effective field theories to higher-point operators. Working in the context of theories polynomial in $X=(\partial ϕ)^2$, we examine how the techniques of bounding such operators based on causality, analyticity of scattering amplitudes, and unitarity of the spectral representation are all modified for operators beyond $(\partial ϕ)^4$. Under weak-coupling assumptions that we clarify, we show using all three methods that in theories in which the coefficient $λ_n$ of the $X^n$ term for some $n$ is larger th…
In this paper the compatibility is analyzed of the non-perturbative equations of state of quarks and gluons arising from the lattice with some natural requirements for self-gravitating objects at equilibrium: the existence of an equation of state (namely, the possibility to define the pressure as a function of the energy density), the absence of superluminal propagation and Le Chatelier's principle. It is discussed under which conditions it is possible to extract an equation of state (in the above sense) from the non-perturbative propagators arising from the fits of the latest lattice data. In…
In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it tu…
The understanding of the non-perturbative regime of YM theories remains a challenging open problem in theoretical physics. Notably, a satisfactory description of the confinement of gluons is not at our disposal so far. In this thesis, the RGZ framework, designed to provide a proper quantization of YM theories by taking into account the existence of the so-called Gribov copies is explored. Successfully introduced in the Landau gauge, the RGZ set up does not extend easily to different gauges. The main reason is that a clear formulation of the analogue of the Gribov horizon in the Landau gauge is…
We investigate the phenomenological consequences of a strict gauge-invariant formulation of the Higgs particle. This requires a description of the observable scalar particle in terms of a bound state structure. Although this seems to be at odds with the common treatment of electroweak particle physics at first glance, the properties of the bound state can be described in a perturbative fashion due to the Fröhlich-Morchio-Strocchi (FMS) framework. In particular a relation between the bound-state Higgs and the elementary Higgs field is obtained within $R_ξ$ gauges such that the main quantitative…
