On Gribov ambiguity in finite temperature Abelian gauge theory

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.

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

Zeitschrift für Physik C Particles and Fields ◽

10.1007/bf01413603 ◽

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

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

International Journal of Modern Physics A ◽

10.1142/s0217751x17501937 ◽

2017 ◽

Vol 32 (33) ◽

pp. 1750193 ◽

Cited By ~ 1

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.

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