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Algebraic spinors and directed random walks in the McKane-Parisi-Sourlas theorem

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Abstract

We present the Dirac propagator as a random walk on anS D−1 sphere for Majorana spinors, even spinor space, Dirac spinors, and Chevalley-Crumeyrolle spinors built from Minkowski space. We propose the Dirac propagator constructed from Chevalley-Crumeyrolle spinors as the generators of a Markov process such that McKane-Parisi-Sourlas theorem can be applied to calculate the expectation values for functions of local times.

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Rodríguez-Romo, S. Algebraic spinors and directed random walks in the McKane-Parisi-Sourlas theorem. Int J Theor Phys 32, 1475–1480 (1993). https://doi.org/10.1007/BF00672850

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Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Random Walk
  • Markov Process