Background field method for nonlinear σ-model in stochastic quantization

1988 ◽  
Vol 305 (3) ◽  
pp. 516-542 ◽  
Author(s):  
Naohito Nakazawa ◽  
Daiji Ennyu
Keyword(s):  
Background Field ◽  
Field Method ◽  
Stochastic Quantization ◽  
Background Field Method

SUPERSPACE FORMULATION OF STOCHASTIC BACKGROUND FIELD METHOD

1989 ◽  
Vol 04 (06) ◽  
pp. 569-579 ◽  
Author(s):  
NAOHITO NAKAZAWA
Keyword(s):  
Background Field ◽  
Field Method ◽  
General Covariance ◽  
Stochastic Quantization ◽  
Stochastic Background ◽  
Background Field Method

We formulate the background field method for a nonlinear σ-model in stochastic quantization based on the superspace formulation. In addition to the general covariance, the BRS invariance of the system is manifestly maintained in our formulation.

scholarly journals NONCOMMUTATIVITY AND NON-ANTICOMMUTATIVITY PERTURBATIVE QUANTUM GRAVITY

2012 ◽  
Vol 27 (13) ◽  
pp. 1250075 ◽  
Author(s):  
MIR FAIZAL
Keyword(s):  
Quantum Gravity ◽  
Lagrangian Density ◽  
Background Field ◽  
Field Method ◽  
Gauge Fixing ◽  
Perturbative Quantum ◽  
Background Field Method

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

scholarly journals FIELD DECOMPOSITION AND THE GROUND STATE STRUCTURE OF SU(2) YANG–MILLS THEORY

2002 ◽  
Vol 17 (25) ◽  
pp. 3681-3688 ◽  
Author(s):  
LISA FREYHULT
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Scalar Fields ◽  
Background Field ◽  
Field Method ◽  
Gauge Fields ◽  
Ground State Structure ◽  
State Structure ◽  
Yang Mills ◽  
Background Field Method

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

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