scholarly journals Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Chris L. Lin ◽  
Carlos R. Ordóñez
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Scale Dependence ◽  
Classical Action ◽  
Loop Expansion ◽  
Background Field Method

We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for anO(N)symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential.

scholarly journals OPTIMIZED POST GAUSSIAN APPROXIMATION IN THE BACKGROUND FIELD METHOD

2004 ◽  
Vol 19 (10) ◽  
pp. 1589-1607 ◽  
Author(s):  
ABDULLA RAKHIMOV ◽  
JAE HYUNG YEE
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Gaussian Approximation ◽  
Background Field ◽  
Field Method ◽  
New Method ◽  
Background Field Method ◽  
Gaussian Effective Potential ◽  
Correction Terms

We have extended the variational perturbative theory based on the background field method to include the optimized expansion of Okopinska and the post Gaussian effective potential of Stansu and Stevenson. This new method provides a much simpler way to compute the correction terms to the Gaussian effective action (or potential). We have also renormalized the effective potential in 3+1 dimensions by introducing appropriate counterterms in the Lagrangian.

scholarly journals FIELD DECOMPOSITION AND THE GROUND STATE STRUCTURE OF SU(2) YANG–MILLS THEORY

2002 ◽  
Vol 17 (25) ◽  
pp. 3681-3688 ◽  
Author(s):  
LISA FREYHULT
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Scalar Fields ◽  
Background Field ◽  
Field Method ◽  
Gauge Fields ◽  
Ground State Structure ◽  
State Structure ◽  
Yang Mills ◽  
Background Field Method

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

A three-dimensional gauge theory

1992 ◽  
Vol 70 (5) ◽  
pp. 301-304 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Gauge Theory ◽  
Scalar Field ◽  
Three Dimensional ◽  
Background Field ◽  
Field Method ◽  
Simons Theory ◽  
Point Function ◽  
Background Field Method ◽  
Chern Simons ◽  
Chern Simons Theory

We investigate a three-dimensional gauge theory modeled on Chern–Simons theory. The Lagrangian is most compactly written in terms of a two-index tensor that can be decomposed into fields with spins zero, one, and two. These all mix under the gauge transformation. The background-field method of quantization is used in conjunction with operator regularization to compute the real part of the two-point function for the scalar field.

scholarly journals A FORMULATION OF THE YANG–MILLS THEORY AS A DEFORMATION OF A TOPOLOGICAL FIELD THEORY BASED ON THE BACKGROUND FIELD METHOD AND QUARK CONFINEMENT PROBLEM

2001 ◽  
Vol 16 (07) ◽  
pp. 1303-1346 ◽  
Author(s):  
KEI-ICHI KONDO
Keyword(s):  
Field Theory ◽  
Magnetic Monopole ◽  
Background Field ◽  
Field Method ◽  
Quark Confinement ◽  
Mass Generation ◽  
Yang Mills ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Background Field Method

By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.

One-loop calculation of the background field quantum-chromodynamic β function

1993 ◽  
Vol 71 (5-6) ◽  
pp. 237-240 ◽  
Author(s):  
M. A. van Eijck
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Background Field ◽  
Landau Gauge ◽  
Field Method ◽  
Gauge Invariant ◽  
Finite Temperature Field Theory ◽  
Background Field Method ◽  
Β Function ◽  
Invariant Quantum

We present a one-loop calculation of a gauge invariant quantum-chromodynamic β function at finite temperature with rules coming from the background field method in the Landau gauge and from the retarded and advanced formulation of finite-temperature field theory.

THE BACKGROUND FIELD METHOD AND THE ANOMALIES OF THE HETEROTIC σ-MODEL IN A CURVED (1, 0) SUPERSPACE

1991 ◽  
Vol 06 (17) ◽  
pp. 2971-2998 ◽  
Author(s):  
S.V. KETOV ◽  
O.A. SOLOVIEV
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Low Energy ◽  
Heterotic String ◽  
Explicit Calculation ◽  
Two Dimensional ◽  
Gauge Bosons ◽  
Background Field Method ◽  
Background Fields

The covariant (in the σ-model sense) background field method for calculating the anomalies of the heterotic string propagating on the background of its massless modes is developed in a curved superspace of the two-dimensional (1, 0) supergravity. As the massless background fields, we use a metric, an antisymmetric tensor, a dilaton and gauge bosons. Explicit calculation of the anomalies up to five loops is performed and the results are found to be in agreement with the known facts about the heterotic string low-energy effective action. The dilaton-dependent corrections to the anomalies at the two- and three-loop levels are shown to be absent.

scholarly journals COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM

1998 ◽  
Vol 13 (20) ◽  
pp. 1623-1635 ◽  
Author(s):  
IOSEPH L. BUCHBINDER ◽  
SERGEI M. KUZENKO
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Vector Multiplet ◽  
Harmonic Superspace ◽  
Background Field Method ◽  
Field Formalism ◽  
The One

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

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