The quantum Hilbert space of a chiral two-form in d = 5 + 1 dimensions

Details The quantum Hilbert space of a chiral two-form in d = 5 + 1 dimensions The quantum Hilbert space of a chiral two-form in d = 5 + 1 dimensions

2001-11-16

arxiv.org/abs/hep-th/0111150v1

JHEP 0203 (2002) 021

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1088/1126-6708/2002/03/021

We consider the quantum theory of a two-form gauge field on a space-time which is a direct product of time and a spatial manifold, taken to be a compact five-manifold with no torsion in its cohomology. We show that the Hilbert space of this non-chiral theory is a certain subspace of a tensor product of two spaces, that are naturally interpreted as the Hilbert spaces of a chiral and anti-chiral two-form theory respectively. We also study the observable operators in the non-chiral theory that correspond to the electric and magnetic field strengths, the Hamiltonian, and the exponentiated holonomy of the gauge-field around a spatial two-cycle. All these operators can be decomposed into contributions pertaining to the chiral and anti-chiral sectors of the theory.

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