Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-07-02
J.Phys.A31:1001-1023,1998
Physics
High Energy Physics
High Energy Physics - Theory
27 pages LateX; published version
Scientific paper
10.1088/0305-4470/31/3/012
We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the particle creation operators in the theory. We find new solutions to the discrete time Dirac equation, referred to as oscillons on account of their extraordinary behaviour. Their principal characteristic is that they oscillate with a period twice that of the fundamental time interval T of our theory. Although these solutions can be associated with definite charge, linear momentum and spin, such objects should not be observable as particles in the continuous time limit. We find that for non-zero T they correspond to states with negative squared norm in Hilbert space. However they are an integral part of the discrete time Dirac field and should play a role in particle interactions analogous to the role of longitudinal photons in conventional quantum electrodynamics.
Jaroszkiewicz George
Norton Keith
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