BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry

Abstract

The quantization of spontaneously broken gauge theories in noncommutative geometry(NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang and Ne'eman recently succeeded in realizing the BRST quantization of gauge theories in NCG in the matrix derivative approach proposed by Coquereaux et al. The present author has proposed a characteristic formulation to reconstruct a gauge theory in NCG on the discrete space $M_4\times Z_{{}_N}$. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST invariant Lagrangian in the same way as Lee, Hwang and Ne'eman and apply it to the SU(2)$\times$U(1) gauge theory.

RevTeX, page 9

References in corpus (6)

• Noncommutative Kaluza-Klein Theory
• BRST Quantization of Gauge Theory in Noncommutative Geometry: Matrix Derivative Approach
• Non-Commutative Differential Geometry and Standard Model
• New Incorporation of the Strong Interaction in NCG and Standard Model
• Reconstruction of the spontaneously broken gauge theory in non-commutative geometry
• Modified Reconstruction of Standard Model in Non-Commutative Differential Geometry

Cited by in corpus (4)

• Noncommutative Quantum Gravity
• Perturbative Quantum Gravity on Complex Spacetime
• Parallel Transport in Gauge Theory on $M_4\times Z_2$ Geometry
• BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry