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Lorentz covariance and kinetic charge

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Abstract

There is a one-to-one correspondence between inequivalent covariant displaced Fock representations of the free relativistic field and the 1-cohomology of the Poincaré group with coefficients in the 1-particle space.

Representations with positive energy are obtained from cocycles with finite energy which have particle-like properties and are interpreted as condensed states of matter without a sharply defined mass.

The 1-cohomology groups ofP ↑+ are calculated. These are trivial in 3- or 4-dimensional space-time, or if the mass is non-zero. Non-trivial cocycles for subgroups lead to representations in whichP-invariance is spontaneously broken. We recoverP-invariance in a direct integral representation possessing a gauge group, and a superselection structure labelled by the velocities of the condensed states of matter which are the cocycles determining each irreducible component of the representation. A model in 4-dimensional space-time is constructed.

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Authors and Affiliations

  1. Department of Mathematics, Bedford College, NW1 4NS, London, England

    P. Basarab-Horwath, R. F. Streater & J. Wright

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  1. P. Basarab-Horwath
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  2. R. F. Streater
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  3. J. Wright
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Communicated by R. Haag

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Basarab-Horwath, P., Streater, R.F. & Wright, J. Lorentz covariance and kinetic charge. Commun.Math. Phys. 68, 195–207 (1979). https://doi.org/10.1007/BF01221124

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  • DOI: https://doi.org/10.1007/BF01221124

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