Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-11-09
Phys.Rev. D53 (1996) 5765-5770
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, LaTex file, one figure (not included)
Scientific paper
10.1103/PhysRevD.53.5765
Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the 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 Feynman diagrams with a given number of internal on-shell free topological 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.
Fainberg Ya. V.
Shikakhwa M. S.
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