A new approach to anomalous axial vector field theory

International Journal of Modern Physics A ◽

10.1142/s0217751x21501049 ◽

2021 ◽

pp. 2150104

Author(s):

A. K. Kapoor

Keyword(s):

Field Theory ◽

Axial Vector ◽

Ultra Violet ◽

Realistic Model ◽

Quantization Scheme ◽

Stochastic Quantization ◽

Gauge Model ◽

Operator Formalism ◽

New Approach ◽

Vector Gauge

In an earlier paper, it has been shown that the ultra violet divergence structure of anomalous [Formula: see text] axial vector gauge model in the stochastic quantization scheme is different from that in the conventional quantum field theory. Also, it has been shown that the model is expected to be renormalizable. Based on the operator formalism of the stochastic quantization, a new approach to anomalous [Formula: see text] axial vector gauge model is proposed. The operator formalism provides a convenient framework for analysis of ultra violet divergences, but the computations in a realistic model become complicated. In this paper a new approach to do computations in the model is formulated directly in four dimensions. The suggestions put forward here will lead to simplification in the study of applications of the axial vector gauge theory, as well as those of other similar models.

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Stochastic quantization of axial vector gauge theories with fermions

Modern Physics Letters A ◽

10.1142/s0217732319501761 ◽

2019 ◽

Vol 34 (22) ◽

pp. 1950176

Author(s):

A. K. Kapoor

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Gauge Theories ◽

Axial Vector ◽

Quantization Scheme ◽

Quantum Field ◽

Stochastic Quantization ◽

Massless Fermion ◽

Fermion Masses ◽

Vector Gauge

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory (CQFT) in higher orders. It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. Some features of U(1) axial vector gauge theory in Parisi Wu stochastic quantization are reported. These features are not absent if the theory is formulated in the conventional way. In particular we present arguments for renormalizability of the massive axial vector gauge theory coupled to a massless fermion.

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A new approach to anomalous axial vector field theory – II

Modern Physics Letters A ◽

10.1142/s0217732321501558 ◽

2021 ◽

pp. 2150155

Author(s):

A. K. Kapoor

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Vector Field ◽

Axial Vector ◽

Quantum Field ◽

Stochastic Quantization ◽

New Approach ◽

Four Dimensions

This work is continuation of a stochastic quantization program reported earlier. In this paper, we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods.

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BRST STOCHASTIC QUANTIZATION

International Journal of Modern Physics A ◽

10.1142/s0217751x91002367 ◽

1991 ◽

Vol 06 (28) ◽

pp. 4985-5015 ◽

Cited By ~ 2

Author(s):

HELMUTH HÜFFEL

Keyword(s):

Field Theory ◽

Particle System ◽

Relativistic Particle ◽

Point Particle ◽

Quantization Scheme ◽

Stochastic Quantization ◽

Quantization Method ◽

Second Quantization ◽

Spinning Particle ◽

Constrained Hamiltonian Systems

After a brief review of the BRST formalism and of the Parisi-Wu stochastic-quantization method, the BRST-stochastic-quantization scheme is introduced. This scheme allows the second quantization of constrained Hamiltonian systems in a manifestly gauge-symmetry-preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed with a discussion on the interacting field theory associated with the relativistic-point-particle system.

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ON STOCHASTIC QUANTIZATION OF WITTEN'S FIELD THEORY OF INTERACTING STRING

Modern Physics Letters A ◽

10.1142/s0217732387000938 ◽

1987 ◽

Vol 02 (10) ◽

pp. 753-759 ◽

Cited By ~ 1

Author(s):

YUAN-BEN DAI ◽

CHUAN-SHENG XIONG ◽

WEI-DONG ZHAO

Keyword(s):

Field Theory ◽

Quantization Scheme ◽

Stochastic Quantization ◽

Feynman Rules

Simple Feynman rules are obtained for Witten's theory of interacting string using stochastic quantization scheme.

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RENORMALIZATION OF STOCHASTICALLY QUANTIZED FIELD THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x88000047 ◽

1988 ◽

Vol 03 (01) ◽

pp. 163-185 ◽

Cited By ~ 2

Author(s):

S. CHATURVEDI ◽

A.K. KAPOOR ◽

V. SRINIVASAN

Keyword(s):

Langevin Equation ◽

Field Theories ◽

Quantization Scheme ◽

Stochastic Quantization ◽

Coupling Constant ◽

Operator Formalism ◽

Four Dimensions ◽

Quantized Field ◽

The One ◽

Renormalization Constants

We discuss the renormalizability of stochastically quantized ϕ4 theory in four dimensions using the operator formalism of the Langevin equation developed by Namiki and Yamanaka. The operator formalism casts the Parisi Wu stochastic quantization scheme into a five-dimensional field theory. The usefulness of this approach over the one based directly on the Langevin equation is brought out for discussion of renormalization. We propose a new regularization scheme for the stochastic diagrams and use it to compute the renormalization constants and counter terms for the ϕ4 theory to second order in the coupling constant.

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Symplectic Quantization I: Dynamics of Quantum Fluctuations in a Relativistic Field Theory

Foundations of Physics ◽

10.1007/s10701-021-00470-9 ◽

2021 ◽

Vol 51 (3) ◽

Author(s):

Giacomo Gradenigo ◽

Roberto Livi

Keyword(s):

Field Theory ◽

General Relativity ◽

Quantum Fluctuations ◽

Time Variable ◽

Quantization Scheme ◽

Stochastic Quantization ◽

Relativistic Invariance ◽

Additional Time ◽

Relativistic Field ◽

Time Quantum

AbstractWe propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021).

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BRST quantization of vector and axial-vector gauge theory

Physical Review D ◽

10.1103/physrevd.48.4916 ◽

1993 ◽

Vol 48 (10) ◽

pp. 4916-4918

Author(s):

Dae Sung Hwang ◽

Chang-Yeong Lee

Keyword(s):

Gauge Theory ◽

Brst Quantization ◽

Axial Vector ◽

Vector Gauge

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On the Modular Operator of Mutli-component Regions in Chiral CFT

Communications in Mathematical Physics ◽

10.1007/s00220-021-04054-6 ◽

2021 ◽

Author(s):

Stefan Hollands

Keyword(s):

Field Theory ◽

Integral Equation ◽

Hilbert Problem ◽

Matrix Elements ◽

New Approach ◽

Conformal Field ◽

The Matrix ◽

Kms Condition ◽

Modular Operator ◽

Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

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