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Quantum theory of particles with spin zero and one half in external fields

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Abstract

The unitary (pseudo unitary) time-evolution operator for a particle with spin half (zero) in an external time-dependent electromagnetic (scalar) field is used to generate a Bogoliubov automorphism on the algebra of the free in field. For the case of an electric external field (scalar field) a finite expression for Ωout is given and theS-matrix constructed. The latter is unitary and implements the Bogoliubov automorphism. Theorems by Shale and Stinespring are rederived.

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Supported in part by the U.S. Atomic Energy Commission under Contract No. AT-30-1-3829.

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Seiler, R. Quantum theory of particles with spin zero and one half in external fields. Commun.Math. Phys. 25, 127–151 (1972). https://doi.org/10.1007/BF01877516

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Keywords

  • Neural Network
  • Statistical Physic
  • Shale
  • Complex System
  • Nonlinear Dynamics