Topological unitarity identities in Chern-Simons theories
- Department of Physics, Middle East Technical University, 06531, Ankara (Turkey)
Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the {ital S} matrix is constructed and seen to be formally the same as that of spinor quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external photon lines excluded, and with the propagator of the topological Chern-Simons photon substituted for the Maxwell photon propagator. It is shown that the absence of real topological photons in the complete set of vector states of the total Hilbert space leads in a given order of perturbation theory to topological unitarity identities that demand the vanishing of the gauge-invariant sum of the imaginary parts of the Feynman diagrams with a given number of internal on-shell free toplogical photon lines. It is also shown that these identities can be derived outside the framework of perturbation theory. The identities are verified explicitly for the scattering of a fermion-antifermion pair in one-loop order. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 284014
- Journal Information:
- Physical Review, D, Vol. 53, Issue 10; Other Information: PBD: May 1996
- Country of Publication:
- United States
- Language:
- English
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