Classical probabilities for Majorana and Weyl spinors

Journal Article · Mon Aug 15 04:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.04.005· OSTI ID:21583328

Wetterich, C ^[1]

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1. Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)

Highlights: > Map of classical statistical Ising model to fermionic quantum field theory. > Lattice-regularized real Grassmann functional integral for single Weyl spinor. > Emerging complex structure characteristic for quantum physics. > A classical statistical ensemble describes a quantum theory. - Abstract: We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q{sub {tau}}(t) for the Ising states {tau}. The time dependent probability distribution of a generalized Ising model obtains as p{sub {tau}}(t)=q{sub {tau}}{sup 2}(t). The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.

• OSTI ID: 21583328
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 8 Vol. 326; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
CRYSTAL MODELS
DISTRIBUTION
FERMIONS
FIELD THEORIES
FUNCTIONS
INTEGRALS
ISING MODEL
MATHEMATICAL MODELS
MATHEMATICS
MECHANICS
PARTICLE PROPERTIES
PROBABILITY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SPIN
SPINORS
STATISTICS
TIME DEPENDENCE
WAVE FUNCTIONS