Four-dimensional commutation relation realizing the local gauge transformation property in the non-abelian gauge theory

1985 ◽  
Vol 28 (3) ◽  
pp. 407-412
Author(s):  
Hiroaki Kanno ◽  
Noboru Nakanishi
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Commutation Relation ◽  
Transformation Property ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Local Gauge ◽  
Local Gauge Transformation

Non-Abelian gauge theory from the Poisson bracket

2018 ◽  
Vol 33 (30) ◽  
pp. 1850182
Author(s):  
Mu Yi Chen ◽  
Su-Long Nyeo
Keyword(s):  
Gauge Theory ◽  
Poisson Bracket ◽  
Commutation Relation ◽  
Maxwell Equations ◽  
Dynamical Variable ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Generalized Poisson ◽  
Lie Algebraic Structure

The Hamiltonian of a nonrelativistic particle coupled to non-Abelian gauge fields is defined to construct a non-Abelian gauge theory. The Hamiltonian which includes isospin as a dynamical variable dictates the dynamics of the particle and isospin according to the Poisson bracket that incorporates the Lie algebraic structure of isospin. The generalized Poisson bracket allows us to derive Wong’s equations, which describe the dynamics of isospin, and the homogeneous (sourceless) equations for non-Abelian gauge fields by following Feynman’s proof of the homogeneous Maxwell equations.It is shown that the derivation of the homogeneous equations for non-Abelian gauge fields using the generalized Poisson bracket does not require that Wong’s equations be defined in the time-axial gauge, which was used with the commutation relation. The homogeneous equations derived by using the commutation relation are not Galilean and Lorentz invariant. However, by using the generalized Poisson bracket, it can be shown that the homogeneous equations are not only Galilean and Lorentz invariant but also gauge independent. In addition, the quantum ordering ambiguity that arises from using the commutation relation can be avoided when using the Poisson bracket.From the homogeneous equations, which define the “electric field” and “magnetic field” in terms of non-Abelian gauge fields, we construct the gauge and Lorentz invariant Lagrangian density and derive the inhomogeneous equations that describe the interaction of non-Abelian gauge fields with a particle.

scholarly journals Local gauge transformation for the quark propagator in an SU(N) gauge theory

2016 ◽  
Vol 93 (7) ◽  
Author(s):  
M. Jamil Aslam ◽  
A. Bashir ◽  
L. X. Gutiérrez-Guerrero
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Quark Propagator ◽  
Local Gauge ◽  
Local Gauge Transformation

scholarly journals The Singular Gauge Transformation in the Non-Abelian Gauge Theory

1978 ◽  
Vol 60 (2) ◽  
pp. 629-630
Author(s):  
J. Sakamoto
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory

CHIRALITY IN ELECTRODYNAMICS

1999 ◽  
Vol 14 (32) ◽  
pp. 5121-5135 ◽  
Author(s):  
G. C. MARQUES ◽  
D. SPEHLER
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Gauge Invariance ◽  
Spinor Field ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Left Right Asymmetry

We show that a not necessarily totally symmetric Bargman–Wigner second rank spinor field is able to accommodate a left–right symmetric U (1)L⊗ U (1)R Abelian gauge theory. We show that some features of the standard QED, such as vectorial gauge invariance, invariance under gauge transformation of the second kind, and the nonexistence of monopoles, follow from imposing left–right asymmetry on the level of self-interaction of the spinorial constituents.

scholarly journals WIGNER'S LITTLE GROUP AND BRST COHOMOLOGY FOR ONE-FORM ABELIAN GAUGE THEORY

2004 ◽  
Vol 19 (16) ◽  
pp. 2721-2737 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Decisive Role ◽  
Decomposition Theorem ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Brst Cohomology ◽  
The Relationship ◽  
Translation Subgroup

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of Wigner's little group for the free one-form Abelian gauge theory in four (3+1)-dimensions (4D) of space–time. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi–Rouet–Stora–Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.

Regge behavior of spontaneously broken non-Abelian gauge theory

1978 ◽  
Vol 17 (2) ◽  
pp. 585-597 ◽  
Author(s):  
J. B. Bronzan ◽  
R. L. Sugar
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Regge Behavior

scholarly journals Static force potential of a non-Abelian gauge theory in a finite box in Coulomb gauge

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Tomohiro Furukawa ◽  
Keiichi Ishibashi ◽  
H. Itoyama ◽  
Satoshi Kambayashi
Keyword(s):  
Gauge Theory ◽  
Coulomb Gauge ◽  
Static Force ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Force Potential

scholarly journals Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

2017 ◽  
Vol 32 (33) ◽  
pp. 1750193 ◽  
Author(s):  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
The Self ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Abelian Theory ◽  
Matter Fields

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

scholarly journals Tailoring Non-Abelian Gauge Theory for Digital Quantum Simulation

2020 ◽  
Author(s):  
Jesse Stryker ◽  
Indrakshi Raychowdhury
Keyword(s):  
Gauge Theory ◽  
Quantum Simulation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory
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