On the complex structure in the Gupta-Bleuler quantization method

TL;DR

This paper investigates the conditions under which a complex structure exists in the Gupta-Bleuler quantization method, focusing on fermionic constraints in various space-time dimensions, with explicit solutions provided for ten dimensions.

Contribution

It identifies the conditions for complex structure existence in Gupta-Bleuler quantization with mixed fermionic constraints and offers explicit solutions for ten-dimensional space-time.

Findings

Complex structure exists under specific conditions for fermionic constraints.

Explicit solution provided for ten-dimensional case.

Highlights importance of dimensions 3 and 10.

Abstract

We examine the general conditions for the existence of the complex structure intrinsic in the Gupta-Bleuler quantization method for the specific case of mixed first and second class fermionic constraints in an arbitrary space-time dimension. The cases d=3 and 10 are shown to be of prime importance. The explicit solution for d=10 is presented.