Renormalization of non-Abelian gauge theories in a background-field gauge. I. Green's functions

1975 ◽  
Vol 12 (2) ◽  
pp. 482-488 ◽  
Author(s):  
H. Kluberg-Stern ◽  
J. B. Zuber
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Background Field ◽  
Abelian Gauge

scholarly journals Composite and Background Fields in Non-Abelian Gauge Models

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1985
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Effective Action ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Systematic Analysis ◽  
Generating Functional ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Background Fields

A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of vertex Green’s functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov–Zwanziger theory.

A study of the path-integral quantization of Abelian gauge theories when no explicit gauge-fixing term is included in the bilinear part of the gauge-field action

1985 ◽  
Vol 63 (10) ◽  
pp. 1334-1336
Author(s):  
Stephen Phillips
Keyword(s):  
Gauge Field ◽  
Path Integral ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Gaussian Form ◽  
Path Integral Quantization ◽  
Field Action ◽  
Gauge Fixing

The mathematical problem of inverting the operator [Formula: see text] as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article.Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, [Formula: see text], can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one.Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action.

Renormalization of Composite Operators in Non-Abelian Gauge Theories

1997 ◽  
Vol 12 (27) ◽  
pp. 4881-4893
Author(s):  
Taeyeon Lee
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Coupling Parameter ◽  
Dimensional Regularization ◽  
Abelian Gauge ◽  
Generating Functional ◽  
Minimal Subtraction Scheme ◽  
Strength Tensor ◽  
Zero Momentum

Renormalization of composite operators (at zero momentum transfer) is discussed in non-Abelian gauge theories. Composite operators are inserted into Green's functions by differentiating Z, the generating functional for Green's functions, with respect to the parameters coupled to the composite operators. In the case of the field strength tensor with no coupling parameter, it is possible to have the form of [Formula: see text] by rescaling gauge fields as Aμa → Aμa/g. Then the renormalization of [Formula: see text] can be carried out by the differentiation [Formula: see text]. By doing this, the renormalization procedure is different from the previous work of Kluberg–Stern and Zuber. The procedure of this paper naturally leads to the proper basis of operators which makes the triangular renormalization matrix. Explicit forms for the relation between bare and renormalized composite operators are presented, with the dimensional regularization and minimal subtraction scheme.

The one-loop Green’s functions of dimensionally reduced gauge theories

Pramana ◽  
1988 ◽  
Vol 30 (3) ◽  
pp. 173-182 ◽  
Author(s):  
S V Ketov ◽  
Y S Prager
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
The One

scholarly journals Green's Functions for Non-Abelian Gauge Fields

1974 ◽  
Vol 52 (6) ◽  
pp. 1946-1952 ◽  
Author(s):  
J. Sakamoto ◽  
A. Sato
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Gauge Fields ◽  
Abelian Gauge

Sp(2) COVARIANT QUANTIZATION OF GAUGE THEORIES

1991 ◽  
Vol 06 (22) ◽  
pp. 2051-2057 ◽  
Author(s):  
P. M. LAVROV
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Brst Quantization ◽  
Covariant Quantization ◽  
Gauge Dependence

The gauge dependence of the Green's functions generating functionals in the framework of extended Lagrangian BRST quantization is investigated.

scholarly journals ON THE STRUCTURE OF QUANTUM GAUGE THEORIES WITH EXTERNAL FIELDS

1998 ◽  
Vol 13 (23) ◽  
pp. 4077-4089 ◽  
Author(s):  
S. FALKENBERG ◽  
B. GEYER ◽  
P. LAVROV ◽  
P. MOSHIN
Keyword(s):  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
External Fields ◽  
Ward Identities ◽  
Gauge Dependence ◽  
General Gauge

We consider generating functionals of Green's functions with external fields in the framework of BV and BLT quantization schemes for general gauge theories. The corresponding Ward identities are obtained, and the gauge dependence is studied.

Erratum: Green's functions of composite operators and bound states in gauge theories

1990 ◽  
Vol 41 (10) ◽  
pp. 3279-3279 ◽  
Author(s):  
V. P. Gusynin ◽  
V. A. Kushnir ◽  
V. A. Miransky
Keyword(s):  
Bound States ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions
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