Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-11-17
Physics
High Energy Physics
High Energy Physics - Theory
25 pages. arXiv admin note: substantial text overlap with arXiv:1102.3586
Scientific paper
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discreteness of particles is traced back to the discreteness of occupation numbers or Ising-spins, while the continuity of the wave function reflects the continuity of the probability distribution for the Ising-spins.
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