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Topological unitarity identities in Chern-Simons theories
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Date
1996-05-15
Author
Fainberg, VY
Shikakhwa, MS
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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 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.
Subject Keywords
Statistics Parameter
,
Boson
,
Systems
,
Mass Term; Constraints
URI
https://hdl.handle.net/11511/64658
Journal
PHYSICAL REVIEW D
DOI
https://doi.org/10.1103/physrevd.53.5765
Collections
Department of Physics, Article
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V. Fainberg and M. Shikakhwa, “Topological unitarity identities in Chern-Simons theories,”
PHYSICAL REVIEW D
, pp. 5765–5770, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64658.