scholarly journals REMOVAL OF VIOLATIONS OF THE MASTER WARD IDENTITY IN PERTURBATIVE QFT

2008 ◽  
Vol 20 (02) ◽  
pp. 119-172 ◽  
Author(s):  
FERDINAND BRENNECKE ◽  
MICHAEL DÜTSCH
Keyword(s):  
Scalar Field ◽  
Ward Identity ◽  
Field Model ◽  
Action Principle ◽  
Renormalization Condition ◽  
Ward Identities ◽  
Scalar Field Model ◽  
Quantum Action ◽  
Field Formalism ◽  
Quantum Action Principle

We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a local interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in ħ, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example, the method is applied to prove the Ward identities of the O(N) scalar field model.

scholarly journals Two-loop application of the Breitenlohner-Maison/’t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hermès Bélusca-Maïto ◽  
Amon Ilakovac ◽  
Paul Kühler ◽  
Marija Mador-Božinović ◽  
Dominik Stöckinger
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Action Principle ◽  
Ward Identities ◽  
Simple Interpretation ◽  
Loop Level ◽  
Full Structure ◽  
Quantum Action ◽  
The One ◽  
Quantum Action Principle

Abstract We apply the BMHV scheme for non-anticommuting γ5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

scholarly journals From scalar field theories to supersymmetric quantum mechanics

2017 ◽  
Vol 32 (12) ◽  
pp. 1750073 ◽  
Author(s):  
D. Bazeia ◽  
F. S. Bemfica
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Scalar Field ◽  
Field Model ◽  
Supersymmetric Quantum Mechanics ◽  
Field Theories ◽  
Quantum Mechanical ◽  
Scalar Field Theory ◽  
Scalar Field Model ◽  
The Subject

In this work, we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here, we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.

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