Relativistic Theory of Discrete Momentum Space and Discrete Space-Time

E. L. Hill
Phys. Rev. 100, 1780 – Published 15 December 1955
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Abstract

An examination is made of the result of restricting translations and Lorentz transformations in space-time to those with rational coefficients. This removes the major defect of Schild's model of discrete space-time by elimination of the lower bound on the relative velocities of reference systems. The theory is formulated in two stages. In the first the energy and momentum components of a particle are restricted to a countable set satisfying the relativistic energy-momentum relation while the space-time variables are continuous. This gives a theory of discrete energy-momentum space in which wave functions are almost periodic functions. In the second stage the space-time variables are restricted to rational values. This leads to the theory of discrete space-time.

  • Received 25 August 1955

DOI:https://doi.org/10.1103/PhysRev.100.1780

©1955 American Physical Society

Authors & Affiliations

E. L. Hill

  • University of Minnesota, Minneapolis, Minnesota

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Issue

Vol. 100, Iss. 6 — December 1955

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