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Relativistic quantum mechanics and quantum field theory with invariant evolution parameter

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Il Nuovo Cimento A (1965-1970)

Summary

Relativistic quantum mechanics with the invariant evolution parameter or historical time τ is reconsidered. The theory is obtained by quantizing the classical theory in which mass is not fixed but enters later as a constant of motion. There are no constraints among the components of the canonical momentumP μ, but the theory is still relativistic and reparametrization invariant. The Feynman propagator of a free particle is obtained in a very elegant way. The theory is then secondly quantized. The Hamiltonian for the τ-evolution is constructed and it is shown that the Heisenberg equations are identical to the field equations. The formalism is manifestly Poincaré covariant at each step and refers in general to the states with indefinite mass. On the mass shell it contains the known results of the relativistic field theory of a free charged particle.

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  17. In a special reference frame in whichn μ=(1,0,0,0,…) we havep μ n μ=p 0=p 0. We use the metric signature (+--- …).

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  1. J. Stefan Institute, University of Ljubljana, Jamova 39, P.P. 100, 61111, Ljubljana, Jugoslavia

    M. Pavšič

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  1. M. Pavšič
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Pavšič, M. Relativistic quantum mechanics and quantum field theory with invariant evolution parameter. Nuov Cim A 104, 1337–1354 (1991). https://doi.org/10.1007/BF02789576

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  • DOI: https://doi.org/10.1007/BF02789576

PACS 11.10

PACS 03.65

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