13961384
The one loop UV divergent structure of U(1) Yang-Mills theory on noncommutative R**4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.
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.
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.
17379629
The noncommutative U(1) Higgs-Kibble model in the enveloping-algebra formalism and its renormalizability
We discuss the renormalizability of the noncommutative U(1) Higgs-Kibble model formulated within the enveloping-algebra approach. We consider both the phase of the model with unbroken gauge symmetry and the phase with spontaneously broken gauge symmetry. We show that against all odds the gauge sector of the model is always one-loop renormalizable at first order in θμν, perhaps, hinting at the existence of a new symmetry of the gauge sector of the model. However, we also show that the matter sector of the model is non-renormalizable whatever the phase.
118419260
SO(10) GUTs with large tensor representations on Noncommutative Space-time
We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a non-supersymmetric SO(10) GUT which has recently been shown to be consistent with all the physics below $M_{GUT}$. The simplicity of our construction --the simplicity of the Yukawa terms, in particular-- stems from the fact that the Higgses of our GUT can be viewed as elements of the Clifford algebra $\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge transformations act by conjugation. The noncommutative GUT we build contains tree-level interactions among different Higgs species that are absent in their ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance. The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time.
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.
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.
120098848
THE DEPENDENCE OF THE TEMPORAL GAUGE GREEN FUNCTIONS ON THE GAUGE-FIXING VECTORS THROUGH BRS SYMMETRY
The UV-divergent part of the one-loop contribution to the vacuum polarization tensor is shown to satisfy the BRS identities governing its dependence on the time-like vector n and the auxiliary space-like vector n′ introduced by the generalized Leibbrandt-Mandelstam (LM) prescription. As far as we know the BRS identity for the n′ dependence cannot be obtained within the pragmatic approach to the LM prescription. In order to circumvent the problem the LM prescription is incorporated into a BRS-invariant action. The BRS identity for n′ provides an example of a situation where terms of order η combine with loop integrals that are singular as η→0 yielding a finite contribution.
17246313
Variational Approximations for Correlation Functions in Quantum Field Theories
Abstract Applying the time-dependent variational principle of Balian and Veneroni, we derive variational approximations for multi-time correlation functions in Φ 4 field theory. We assume first that the initial state is given and characterized by a density operator equal to a Gaussian density matrix. Then, we study the more realistic situation where only a few expectation values are given at the initial time and we perform an optimization with respect to the initial state. We calculate explicitly the two-time correlation functions with two and four field operators at equilibrium in the symmetric phase.
120311682
The three-gluon vertex in the temporal-planar gauge with the Leibbrandt-Vienna prescription: The one-loop effective action
Abstract The UV-divergent part of the one-loop contribution to the three-gluon vertex, Γμνϱabc, is computed in the temporal-planar gauge. The generalized Leibbrandt-Mandelstam (or Leibbrandt-Vienna) prescription - which is free from the inconsistencies that are known to affect the principal value prescription - is used to define the unphysical poles 1/(k·n)j. We compute the (one-loop) UV-divergent part of the gauge-field effective action up to order g3. We show that all the awkward non-local divergences can be written as the BRS variation of some functional X whereas the β-function coincides with the usual (covariant) result. In the homogeneous case we show that a non-local renormalization of the gauge field Aμa of the form A 0μ a = Z g − 1 2 A μ a − h ƒ μ a (A), A 0μ a and A μ a having identical gauge transformations, and the usual coupling constant renormalization, g0 = Zgμ2ϵg, suffice to get rid of all the UV-divergences in Γμνϱabc and the vacuum polarization tensor gPμνab.
15154154
Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory
We study quantum Chern-Simons theory as the large-mass limit of the limit D --> 3 of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift k --> k + c(v), k being the bare Chern-Simons parameter. In passing, we also prove by explicit computation that topologically massive Yang Mills theory is UV finite.