Ghosts as Negative Spinors

Details Ghosts as Negative Spinors Ghosts as Negative Spinors

2002-07-11

arxiv.org/abs/hep-th/0207110v1

Nucl.Phys. B645 (2002) 371-386

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, no figures, Latex2e

Scientific paper

10.1016/S0550-3213(02)00636-3

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.

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