118569185
Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups
We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter θ. We show that, if the second-degree Casimir has the same value for all the irreducible group representations furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, θ and the fields, along with the inclusion of θ-dependent counterterms which vanish upon imposing the equations of motion. These θ-dependent counterterms have no physical effect since they vanish on-shell. This result along with the vanishing of the UV divergent part of the fermionic four-point functions leads to the unexpected conclusion that the one-loop matter sector of the background-field effective action of these theories is one-loop multiplicatively renormalisable on-shell. We also show that the background-field effective action of the gauge sector of the theories considered here receives no θ-dependent UV divergent contributions at one-loop. We thus conclude that these theories are on-shell one-loop multiplicatively renormalisable at first order in θ.
122147161
The light-cone gauge, Chern-Simons theory and topologically massive Yang-Mills theory
Abstract In this paper, we complete our study of one-loop perturbative Chern-Simons theory in the light-cone gauge n · A a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, which defines Chern-Simons theory as the large-mass limit of a topologically massive field theory, we evaluate the three-point function Λ μνω abc ( p 1 , p 2 , p 3 ) to one loop. The spurious poles of ( q · n ) −1 in the gauge propagator are treated with the n μ ∗ - prescription . It is shown that the vertex function, which contains both local and nonlocal terms, is UV finite, respects the Ward identity and agrees with the one-loop effective action proposed in the preceding paper.
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.
117863195
Chiral gauge anomalies on noncommutative space-time
The consistent form and the covariant form of the gauge anomaly for fundamental U(N) chiral fermions on even-dimensional noncommutative space-time are computed and discussed.
17165052
Shift versus no-shift in local regularizations of Chern-Simons theory
Abstract We consider a family of local BRS-invariant higher covariant derivative regularizations of SU ( N ) Chern-Simons theory that do not shift the value of the Chern-Simons parameter k to k + sign ( k ) c v at one loop.
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.
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.
17341915
Self similar solutions of the evolution equation of a scalar field in an expanding geometry
Abstract We consider the functional Schrodinger equation for a self interacting scalar field in an expanding geometry. By performing a time dependent scale transformation on the argument of the field we derive a functional Schrodinger equation whose hamiltonian is time independent but involves a time-odd term associated to a constraint on the expansion current. We study the mean field approximation to this equation and generalize in this case for interacting fields, the solutions worked out by Bunch and Davies for free fields.
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.
120228894
Perturbative Chern-Simons theory in the light cone gauge: The One loop vacuum polarization tensor in a gauge invariant formalism
Abstract Perturbative Chern-Simons (CS) theory, with gauge group SU( N ), is studied in the physical light-cone gauge n σ A σ a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, we compute the vacuum polarization tensor to one-loop order. The regularized theory is consistent with BRS invariance. It is shown that the vacuum polarization tensor is UV finite and transverse, but contains one non-local term which is strictly gauge-dependent. A finite, non-multiplicative (gauge-dependent) wave function renormalization enables us to express the one-loop effective action as Γ one-loop ( A μ (ren) , k ) = (( k + sign( k ) c v )/4 π ) S CS ( A μ (ren) , where S CS is the classical action and k is the bare Chern-Simons parameter.