Ghosts as Negative Spinors

TL;DR

This paper explores the properties of a BRST ghost as a negative spinor, demonstrating its role as a negative entropy carrier and its representation within SU(2), revealing cancellation effects with positive spin representations.

Contribution

It introduces a novel representation of a ghost as a negative spinor with spin -1/2, and analyzes its algebraic properties and cancellation with positive spin representations.

Findings

Ghost has negative entropy and spin -1/2.

The Casimir operator is nilpotent and equals the BRST operator.

Positive and negative spin representations cancel, resulting in an effective dimension of 1/2.

Abstract

We study the the properties of a BRST ghost degree of freedom complementary to a two-state spinor. We show that the ghost may be regarded as a unit carrier of negative entropy. We construct an irreducible representation of the su(2) Lie algebra with negative spin, equal to -1/2, on the ghost state space and discuss the representation of finite SU(2) group elements. The Casimir operator J^2 of the combined spinor-ghost system is nilpotent and coincides with the BRST operator Q. Using this, we discuss the sense in which the positive and negative spin representations cancel in the product to give an effectively trivial representation. We compute an effective dimension, equal to 1/2, and character for the ghost representation and argue that these are consistent with this cancellation.