Fermions in a space with some extra dimensional reflection symmetries are considered. In this space only one Kaluza-Klein mode is observed at the scales larger than the sizes of the extra dimensions while at the smaller scales all modes become observable. The resulting picture suggests that this model has a built-in Pauli-Villars-like regularization as its inherent characteristic.
We calculate the $U(1)$ axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli-Villars regulator field in the noncommutative QED. Pauli-Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.
In this letter we argue that there is no ambiguity between the Pauli-Villars and other methods of regularization in (2+1)-dimensional quantum electrodynamics with respect to dynamical mass generation, provided we properly choose the couplings for the regulators.
The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar $λφ^4$ field theory and Yukawa-type model are used. We give also an example of nonperturbative calculation in the theory with Pauli-Villars fields, using for that a model of anharmonic oscillator modified by inclusion of ghost variables playing the role similar to Pauli-Villars fields.
It is interesting to superimpose the Pauli-Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation among Pauli-Villars regulators in the continuum limit. A subtlety in Frolov-Slavnov's scheme for an odd number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators,…
A manifestly gauge invariant formulation of chiral theories with fermions on the lattice is developed. It combines SLAC lattice derivative \cite{DWY}, \cite{ACS}, \cite{S} and generalized Pauli-Villars regularization \cite{FS}. The theory is free of fermion doubling, requires only local gauge invariant counterterms and produces correct results when applied to exactly solvable two dimensional models.
It is shown that, in QED$_{3}$, the Pauli-Villars regularization involving a pair of auxiliary fermion fields with masses of opposite sign leads to results that are consistent with those obtained using all other parity-preserving schemes of regularization. At the same time, ambiguity problems remain unsolved in non-Abelian models (QCD$_{3}$).
The combined method of Higher Covariant Derivatives and Pauli-Villars regularization to regularize pure Yang-Mills theories is formulated in the framework of Batalin and Vilkovisky. However, BRS invariance is broken by this method and suitable counterterms should be added to restore it. The one loop counterterm is presented. Contrary to the scheme of Slavnov, this method is regularizing and leads to consistent renormalization group functions, which are the same as those found by other regularization schemes.
It is shown that the one-loop quadratic divergences of standard supergravity can be regulated by the introduction of heavy Pauli-Villars fields belonging to chiral and abelian gauge multiplets. The resulting one-loop correction can be interpreted as a renormalization of the Kähler potential. Regularization of the dilaton couplings to the Yang-Mills sector requires special care, and may shed some light on chiral/linear multiplet duality of the dilaton supermultiplet.
We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter $a$ associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale $Λ$, i.e. $a = 1/Λ$. Solving …
We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex vector. The gauge is fixed by means of the unusual gauge-fixing that gives the same effective action as in the context of the background field method. Indeed, with the background field method it is simple to see that the regularization effectively works. On the other hand, we show that in the usual formalism (non background) the regularization ca…
In the generalized Pauli-Villars regularization of chiral gauge theory proposed by Frolov and Slavnov , it is important to specify how to sum the contributions from an infinite number of regulator fields. It is shown that an explicit sum of contributions from an infinite number of fields in anomaly-free gauge theory essentially results in a specific choice of regulator in the past formulation of covariant anomalies. We show this correspondence by reformulating the generalized Pauli- Villars regularization as a regularization of composite current operators. We thus naturally understand why the …
We propose a solution to the problem of renormalizing light-cone Hamiltonian theories while maintaining Lorentz invariance and other symmetries. The method uses generalized Pauli--Villars regulators to render the theory finite. We discuss the method in the context of Yukawa theory at one loop and for a soluble model in 3+1 dimensions. The model is studied nonperturbatively. Numerical results obtained with use of discretized light-cone quantization, special integration weighting factors, and the complex symmetric Lanczos diagonalization algorithm compare well with the analytic answers.
We address the problem of nonperturbative calculations on the light front in quantum field theory regularized by Pauli-Villars method. As a preliminary step we construct light front Hamiltonians in (2+1)-dimensional $λϕ^4$ model, for the cases without and with spontaneous symmetry breaking. The renormalization of these Hamiltonians in Pauli-Villars regularization is carried out via comparison of all-order perturbation theory, generated by these Hamiltonians, and the corresponding covariant perturbation theory in Lorentz coordinates.
The renormalization problem of (2+1)-dimensional Yang-Mills theory quantized on the light front is considered. Extra fields analogous to those used in Pauli-Villars regularization are introduced to restore perturbative equivalence between such quantized theory and conventional formulation in Lorentz coordinates. These fields also provide necessary ultraviolet regularization to the theory. Obtained results allow to construct renormalized Hamiltonian of the theory on the light front.
Dynamical symmetries of Born-Infeld theory can be absorbed into the spacetime geometry, giving rise to relativistic kinematics with an additional invariant acceleration scale. The standard Poincare group P is thereby enhanced to its pseudo-complexified version, which is isomorphic to P x P. We construct the irreducible representations of this group, which yields the particle spectrum of a relativistic quantum theory that respects a maximal acceleration. It is found that each standard relativistic particle is associated with a `pseudo'-partner of equal spin but generically different mass. These…
We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentz- and CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the nonperturbative theory appears to generate a definite value. However, the CPT-even radiative corrections in this same formulation of the theory generally break gauge invariance. We show that gauge invariance may yet be preserved through the use of a Pauli-Villars regulator, and, contrary to earlier expectations, this regulator does not necessarily give rise to a vanish…
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
It is shown that the one-loop ultraviolet divergences in renormalizable supersymmetric theories can be regulated by the introduction of heavy Pauli-Villars chiral supermultiplets, provided the generators of the gauge group are traceless in the matter representation. The procedure is extended to include supersymmetric gauged nonlinear sigma models.
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev--Popov ghosts then establishes a residual BRST symmetry. Although there are drawba…
We study the regularization and renormalization of the Yang-Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli-Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov's method, does not appear in our scheme, and the well-known vale of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of $Λ^0$ and $Λ^{-4}$. These results are the…
We regularize QCD using the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Slavnov. It is known that for pure Yang-Mills theory the Pauli-Villars determinants generate unphysical logarithmic radiative corrections at one loop that modify the beta function. Here we prove that when the gauge fields are coupled to fermions so that one has QCD, these unphysical corrections translate into a violation of unitarity. We provide an understanding of this by seeing that Slavnov's choice for the Pauli-Villars determinants introduces extra propagating degrees of freed…
The proper-time regularization of bosonic string reproduces the results of canonical quantization in a special scaling limit where the length in target space has to be renormalized. We repeat the analysis for the Pauli-Villars regularization and demonstrate the universality of the results. In the mean-field approximation we compute the susceptibility anomalous dimension and show it equals 1/2. We discuss the relation with the previously known results on lattice strings.
We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.
We extend the idea of the generalized Pauli-Villars regularization of Frolov and Slavnov and analyze the general structure of the regularization scheme. The gauge anomaly-free condition emerges in a simple way in the scheme, and, under the standard prescription for the momentum assignment, the Pauli-Villars Lagrangian provides a gauge invariant regularization of chiral fermions in arbitrary anomaly-free representations. The vacuum polarization tensor is transverse, and the fermion number and the conformal anomalies have gauge invariant forms. We also point out that the real representation can …
We extend the QCD Lagrangian to include Pauli-Villars (PV) gluons, quarks, and ghosts in such a way as to retain BRST invariance in an arbitrary covariant gauge. The extended Lagrangian can provide a starting point for nonperturbative calculations in QCD, particularly with light-front techniques, and the methods used to construct it may be useful for perturbative calculations in theories where dimensional regularization is not viable. The regularization is arranged by having all interaction terms in the Lagrangian be couplings between null fields, specific combinations of positive and negative…
We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli-Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. …
It is shown that the one-loop coefficients of on-shell operators of standard supergravity with canonical gauge kinetic energy can be regulated by the introduction of Pauli-Villars chiral and abelian gauge multiplets, subject to a condition on the matter representations of the gauge group. Aspects of the anomaly structure of these theories under global nonlinear symmetries and an anomalous gauge symmetry are discussed.
We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli-Villars fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, we also discuss how perturbation theory in the difference b…
Abelian anomaly is examined by means of the recently proposed gauge invariant regularization for SO(10) chiral gauge theory and its generalization for a theory of arbitrary gauge group with anomaly-free chiral fermion contents. For both cases it is shown that the anomaly with correct normalization can be obtained in a gauge invariant form without any counterterms.
When the path integral method of anomaly evaluation is applied to chiral gauge theories, two different types of gauge anomaly, i.e., the consistent form and the covariant form, appear depending on the regularization scheme for the Jacobian factor. We clarify the relation between the regularization scheme and the Pauli--Villars--Gupta (PVG) type Lagrangian level regularization. The conventional PVG, being non-gauge invariant for chiral gauge theories, in general corresponds to the consistent regularization scheme. The covariant regularization scheme, on the other hand, is realized by the genera…
We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not $-11/3,$ as it should be, but $-23/6.$ The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization me…
We review the history of the ghost problem in quantum field theory from the Pauli-Villars regulator theory to currently popular fourth-order derivative quantum gravity theories. While these theories all appear to have unitarity-violating ghost states with negative norm, we show that in fact these ghost states only appear because the theories are being formulated in the wrong Hilbert space. In these theories the Hamiltonians are not Hermitian but instead possess an antilinear symmetry. Consequently, one cannot use inner products that are built out of states and their Hermitian conjugates. Rathe…
On-shell Pauli-Villars regularization of the one-loop divergences of supergravity theories is used to study the anomaly structure of supergravity and the cancellation of field theory anomalies under a $U(1)$ gauge transformation and under the T-duality group of modular transformations in effective supergravity theories with three Kähler moduli $T^i$ obtained from orbifold compactification of the weakly coupled heterotic string. This procedure requires constraints on the chiral matter representations of the gauge group that are consistent with known results from orbifold compactifications. Paul…
We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the LW premise that unstable particles can be removed from the sets of incoming and outgoing states in scattering processes. The removal leads to a non-Hermitian classical limit, besides clashing with the observation of the muon. If, on the other hand, all the states are included, the LW models have a Hamiltonian unbounded from below or negative norms. Purely virtual particles, on the contrary, lead to a Hermitian classical limit and are ab…
We use Pauli-Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli-Villars chiral multiplets can be chosen in such a way that the anomaly is universal in the sense that its coefficient depends only on a single holomorphic function of the three diagonal moduli. It is therefore possible to cancel the anomaly by a generalization of the four-dimensional Green-Schwarz mechanism. In particular we are able to reproduce the results of a string…
Taking the induced action for gauge fields coupled to affine currents as an example, we show how loop calculations in non-local two-dimensional field theories can be regulated. Our regularisation method for one loop is based on the method of Pauli and Villars. We use it to calculate the renormalisation factors for the corresponding effective actions, clearing up some discrepancies in the literature. In particular, it will be shown explicitly that vector gauge transformation invariance and Haar invariance of functional integral measures impose different requirements, but they are related by a c…
The one-loop structure of the trace anomaly is investigated using different regularizations and renormalization schemes: dimensional, proper time and Pauli-Villars. The universality of this anomaly is analyzed from a very general perspective. The Euler and Weyl terms of the anomalous trace of the stress tensor are absolutely universal. The pure derivative $ \square R$-term is shown to be universal only if the regularization breaks conformal symmetry softly. If the breaking of conformal symmetry by the regularization method is hard the coefficient of this term might become arbitrary which point…
We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction…
It is demonstrated that in the (2+1)-dimensional topologically massive gauge theories an agreement of the Pauli-Villars regularization scheme with the other schemes can be achieved by employing pairs of auxiliary fermions with the opposite sign masses. This approach does not introduce additional violation of discrete (P and T) symmetries. Although it breaks the local gauge symmetry only in the regulator fields' sector, its trace disappears completely after removing the regularization as a result of superrenormalizability of the model. It is shown also that analogous extension of the Pauli-Vill…
We regularize the 3-D quantum electrodynamics by a parity invariant Pauli-Villars regularization method. We find that in the perturbation theory the Chern-Simons term is not induced in the massless fermion case and induced in the massive fermion case.
We show that a choice of Pauli-Villars regulators allows the cancellation of all conformal and chiral anomalies in an effective field theory from Z_3 compactification of the heterotic string with two Wilson lines and an anomalous U(1).
A new version of application Pauli-Villars regularized Green functions in the quantum field theory using higher derivatives is proposed. In this version the regularizing mass $M$ is large but finite. Our approach is demonstrated and discussed on the example of QED. It is shown that in our case there are no ultraviolet divergences and - on the example of the selfenergy spinor Feynman diagram - no infrared ones.
The divergence of the photon self - energy diagram in spinor quantum electrodynamics in $(2+1)$ dimensional space time- $(QED_3)$ is studied by the Pauli - Villars regularization and dimensional regularization. Results obtained by two different methods are coincided if the gauge invariant of theory is considered carefully step by step in these calculations.
Pauli-Villars regularization of Yang-Mills theories and of supergravity theories is outlined, with an emphasis on BRST invariance. Applications to phenomenology and the anomaly structure of supergravity are discussed.
In this paper we study the axial anomaly in Very Special Relativity Electrodynamics using Pauli-Villars and dimensional regularization of ultraviolet divergences and Mandelstam-Leibbrandt regularization of infrared divergences. We compute the anomaly in 2 and 4 dimensional space-time. We find that this procedure preserves the vector Ward identity(charge conservation) and reproduce the standard axial anomaly in 2 and 4 dimensions without corrections from VSR. Finally, we show how to obtain the anomaly in the path integral approach.
The Schwinger-de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space-time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli-Villars and zeta-function regularisation methods, respectively.
The determinant and higher loop terms, usually treated with the Pauli-Villars and higher covariant derivatives methods, in the background field method in 4 dimensions can hardly be regularized simultaneously. At the same time we observe that introduction of a scalar multiplier at the quadratic form, which is equivalent to a change of the measure in the functional integral, influences only the determinant part of the effective action. This allows one to choose the integration measure and the function in the regularized propagator in such a way as to make all terms in the expansion finite.
Using a regularisation of the chiral SU(2) Yang-Mills model by an infinite number of Pauli-Villars fields the doubler free gauge invariant lattice model is constructed. Its continuum limit provides the recently proposed mechanism for cancelation of Witten anomaly.
With a view toward application of the Pauli-Villars regularization method to the Casimir energy of boundaries, we calculate the expectation values of the components of the stress tensor of a confined massive field in 1+1 space-time dimensions. Previous papers by Hays and Fulling are bridged and generalized. The Green function for the time-independent Schrodinger equation is constructed from the Green function for the whole line by the method of images; equivalently, the one-dimensional system is solved exactly in terms of closed classical paths and periodic orbits. Terms in the energy density …
The meson static properties are investigated in Pauli-Villars regularized Nambu--Jona-Lasinio model in strong magnetic field. The quark dimension reduction leads to not only the magnetic catalysis effect on chiral symmetry restoration but also a sudden jump of the mass of the Goldstone mode at the Mott transition temperature.
We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology $\mathbb{R}^3 \times S^1$ and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian $U(1)$ gauge fields $A_μ(x)$ which depend on all four spacetime coordinates (including the coordinate $x^{4}\in S^1$ of the compact dimension) and have vanishing components $A_{4}(x)$ (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorent…
We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an {\it ansatz} in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and t…
