118578498
Remarks on the Renormalisation of Fermions Coupled to Gauge Fields in the Zwanziger Gauge
The renormalisation of fermions coupled to gauge fields in the Stochastic Quantisation formalism is not a trivial subject. In order to simplify the discussion we shall consider QED in the Zwanziger gauge. It shall become clear that the conclusions we will get applies to the non-abelian case as well.
122604338
Nonlocalities in field theory
It has been known since the early 1980's that the computation of light-cone gauge Feynman integrals in the nμ∗ prescription yields both local and nonlocal ultraviolet divergences. Nevertheless, it was recently claimed that the nonlocal contributions to the Yang-Mills vacuum polarization tensor arise from application of the decomposition formula [q·n(q+p)·n]−1=(p·n)−1{−[(q+p)·n]−1+(q·n)−1}, p·n≠0. The purpose of this paper is to show that nonlocal ultraviolet divergences automatically appear in light-cone gauge Feynman integrals defined by the nμ∗ prescription, regardless whether the above decomposition formula is employed or not.
15512478
Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)
U(1) gauge theory on non-commutative Minkowski spacetime in the Feynman–'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism — producing UV charge anti-screening — prevailing over diamagnetism — giving rise to UV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.
119536533
Axial gauge Chern-Simons theory in the Leibbrandt-Mandelstam prescription for a certain class of UV regulators
Abstract We show that the complete perturbative effective action of an SU ( N ) Chern-Simons theory in an homogenous axial-type gauge ( nA a =0, n 2 >0, n 2 n 2 =0) with the generalized Leibbrandt-Mandelstam prescription is the tree-level action for a certain class of regulators. The Gauss linking number is expressed in terms of the axial propagators for the gauge fields.
120724746
DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES
We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.
118725047
BRS techniques applied to the temporal-planar gauge with the vienna prescription: The dependence on the axial vectors
18503987
Anomaly freedom in Seiberg-Witten noncommutative gauge theories
We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the epsilon(mu1mu2mu3mu4) part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter theta(munu). And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.
15588873
Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions
We show at one loop and first order in the noncommutativity parameters that in any noncommutative GUT inspired theory the total contribution to the fermionic four point functions coming only from the interaction between fermions and gauge bosons, though not UV finite by power counting, is UV finite at the end of the day. We also show that this is at odds with the general case for noncommutative gauge theories - chiral or otherwise - defined by means of Seiberg-Witten maps that are the same - barring the gauge group representation - for left-handed spinors as for right-handed spinors. We believe that the results presented in this paper tilt the scales to the side of noncommutative GUTS and noncommutative GUT inspired versions of the standard model.
16042630
CHIRAL GAUGE ANOMALIES ON NONCOMMUTATIVE MINKOWSKI SPACE–TIME
Chiral gauge anomalies on noncommutative Minkowski space–time are computed and have their origin elucidated. The consistent form and the covariant form of the anomaly are obtained. Both Fujikawa's method and Feynman diagram techniques are used to carry out the calculations.
121374470
Fermionic langevin equations without kernel and Zwanzinger's gauge fixing procedure☆
Abstract We study the compatibility of Zwanzinger's gauge fixing procedure and the Langevin equations without kernel for massive fermions from the renormalization theory point of view. The UV divergent part of the QED fermionic propagator is computed at the one-loop level. The problems encountered in its subtraction are analyzed.
11076298
The BRS invariance of noncommutative U(N) Yang–Mills theory at the one-loop level
Abstract We show that U(N) Yang–Mills theory on noncommutative Minkowski spacetime can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov–Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order ℏ , for the MS renormalized noncommutative U(N) Yang–Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.