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.

Gauge theories at finite temperature and the background field method

1990 ◽  
Vol 242 (3-4) ◽  
pp. 412-414 ◽  
Author(s):  
J. Antikainen ◽  
M. Chaichian ◽  
N.R. Pantoja ◽  
J.J. Salazar
Keyword(s):  
Finite Temperature ◽  
Gauge Theories ◽  
Background Field ◽  
Field Method ◽  
Background Field Method

scholarly journals Three-loop Yang–Mills β-function via the covariant background field method

2003 ◽  
Vol 657 ◽  
pp. 257-303 ◽  
Author(s):  
Jan-Peter Börnsen ◽  
Anton E.M. van de Ven
Keyword(s):  
Background Field ◽  
Field Method ◽  
Yang Mills ◽  
Background Field Method ◽  
Β Function

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.

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 Two-loop renormalisation of gauge theories in 4D implicit regularisation and connections to dimensional methods

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
A. Cherchiglia ◽  
D. C. Arias-Perdomo ◽  
A. R. Vieira ◽  
M. Sampaio ◽  
B. Hiller
Keyword(s):  
Quantum Electrodynamics ◽  
Dimensional Regularization ◽  
Background Field ◽  
Field Method ◽  
Loop Order ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Lorentz Algebra ◽  
Background Field Method

AbstractWe compute the two-loop $$\beta $$ β -function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.

scholarly journals Background field method at finite temperature and density

2006 ◽  
Vol 635 (4) ◽  
pp. 213-217 ◽  
Author(s):  
M. Loewe ◽  
S. Mendizabal ◽  
J.C. Rojas
Keyword(s):  
Finite Temperature ◽  
Background Field ◽  
Field Method ◽  
Background Field Method

Evolution of Coupling Constant in Hot QCD

1997 ◽  
Vol 06 (01) ◽  
pp. 45-64
Author(s):  
M. Chaichian ◽  
M. Hayashi
Keyword(s):  
Finite Temperature ◽  
Lorentz Invariance ◽  
Background Field ◽  
Field Method ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Time Formalism ◽  
Background Field Method ◽  
The One

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the breakdown of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite temperature.

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