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Foundations of Physics

, Volume 21, Issue 8, pp 905–929 | Cite as

An application of functional equations to the analysis of the invariance identities of classical gauge field theory

  • David Stapleton
Article
  • 44 Downloads

Abstract

The equations of motion for a particle in a classical gauge field are derived from the invariance identities 2 and basic assumptions about the Lagrangian. They are found to be consistent with the equations of some other approaches to classical gauge-field theory, and are expressed in terms of a set of undetermined functions Eα. The functions Eα are found to satisfy a system of differential equations which has the same formal structure as a system of equations from Yang-Mills theory. 3

These results are obtained by a new method which applies techniques from the theory of functional equations to deduce the way in which the arguments of the Lagrangian must combine. The method constitutes an aid for obtaining the equations of motion when a non-gauge-invariant Lagrangian is chosen, and it is assumed that the equations of motion can be written in a gauge-invariant manner.

Keywords

Differential Equation Field Theory Functional Equation Formal Structure Basic Assumption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. K. Wong, “Field and particle equations for the classical Yang-Mills field and particles with isotopic spin,”Nuovo Cimento A 65, 691–693 (1970).Google Scholar
  2. 2.
    H. Rund, “Differential-geometric and variational background of classical gauge field theories,”Aequ. Math. 24, 132–138 (1982).Google Scholar
  3. 3.
    W. Drechsler and M. E. Mayer,Fiber Bundle Techniques in Gauge Theories (Lecture Notes in Physics) (Springer-Verlag, Berlin, 1977).Google Scholar
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    J. Aczel,Lectures on Functional Equations and Their Applications (Academic, New York, 1966).Google Scholar
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    D. Stapleton, “A technique for the analysis of the invariance identities of classical gauge field theory by means of functional equations,” Ph.D. Dissertation, University of Arizona, Department of Applied Mathematics, 1990.Google Scholar
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    H. Rund, “Invariance identities associated with finite gauge transformations and the uniqueness of the equations of motion of a particle in a classical gauge field,”Found. Phys. 13, 113 (1983).Google Scholar
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    Ibid.,. p. 113.Google Scholar
  8. 8.
    Ref. 1,. pp. 691–693.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • David Stapleton
    • 1
  1. 1.ACTA Inc.Torrance

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