A self-consistent approach to quantum field theory for extended particles

Foundations of Physics 11 (5-6):355-382 (1981)
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Abstract

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis

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References found in this work

The Physical Principles of the Quantum Theory: Transl. Into Engl. By Carl Eckart and Frank C. Hoyt.Werner Heisenberg - 1930 - Chicago: Ill., The University of Chicago Press. Edited by Carl Eckart & Frank Clark Hoyt.
The Principle of Relativity.Albert Einstein - 1920 - [Calcutta]: Dover Publications. Edited by H. Minkowski, Meghnad Saha & Satyendranath Bose.
Relativistic kinematics.Henri Arzeliès - 1966 - New York,: Pergamon Press.

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