Ghosts as Negative Spinors
نویسنده
چکیده
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 −12 , on the ghost state space and discuss the representation of finite SU(2) group elements. The Casimir operator J2 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 12 , and character for the ghost representation and argue that these are consistent with this cancellation.
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