Canonical quantization of gauge fields in the axial gauge with indefinite metric: Basic formulation for perturbation calculation

1980 ◽  
Vol 22 (4) ◽  
pp. 982-992
Author(s):  
Ikuo Ichinose ◽  
Katsushi Sera
Keyword(s):  
Canonical Quantization ◽  
Gauge Fields ◽  
Indefinite Metric ◽  
Perturbation Calculation ◽  
Axial Gauge

scholarly journals ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

Covariant Regularization of Nonlinear Spinorfield Quantum Theories and Probability Interpretation

2000 ◽  
Vol 55 (3-4) ◽  
pp. 415-432
Author(s):  
Harald Stumpf
Keyword(s):  
State Space ◽  
Quantum Dynamics ◽  
Physical State ◽  
Canonical Quantization ◽  
Decomposition Theorem ◽  
Auxiliary Field ◽  
Indefinite Metric ◽  
Current Conservation ◽  
Quantum Theories ◽  
Effective Dynamics

Abstract By a decomposition theorem a higher order nonlinear spinorfield equation can be transformed into a set of first order nonlinear spinorfield equations, i. e. into an auxiliary field formulation which allows canonical quantization. The quantum dynamics of the auxiliary fields is expressed in algebraic Schrödinger representation and admits only unphysical state spaces with indefinite metric. Regularization of the classical theory is transferred into quantum field theory by a noninvertible map from the corresponding auxiliary field state space into an associated physical state space, the metric of which is positive definite. For the effective dynamics in the physical state space probability current conservation is proved, and for physical states which describe composite particle configurations the existence of the state space is demonstrated

scholarly journals Dirac, Majorana, Weyl in 4D

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 111
Author(s):  
Loriano Bonora ◽  
Roberto Soldati ◽  
Stav Zalel
Keyword(s):  
Feynman Diagram ◽  
The Other ◽  
Gauge Fields ◽  
Majorana Fermions ◽  
Diagram Method ◽  
Axial Gauge ◽  
Definition Of ◽  
Weyl Fermions

This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4D. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularisations. Among various well known results we stress in particular the regularisation independence in perturbative approaches, while not all the regularisations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.

scholarly journals Magnetism and anomalous transport in the Weyl semimetal PrAlGe: possible route to axial gauge fields

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Daniel Destraz ◽  
Lakshmi Das ◽  
Stepan S. Tsirkin ◽  
Yang Xu ◽  
Titus Neupert ◽  
...  
Keyword(s):  
Anomalous Transport ◽  
Gauge Fields ◽  
Axial Gauge ◽  
Weyl Semimetal

scholarly journals Canonical Quantization of Non-Abelian Gauge Fields

1976 ◽  
Vol 55 (5) ◽  
pp. 1631-1648 ◽  
Author(s):  
R. Utiyama ◽  
J. Sakamoto
Keyword(s):  
Canonical Quantization ◽  
Gauge Fields ◽  
Abelian Gauge
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