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

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Abstract

The equations of motion for a particle in a classical gauge field are derived from the invariance identities2 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.

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References

  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).

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  2. H. Rund, “Differential-geometric and variational background of classical gauge field theories,”Aequ. Math. 24, 132–138 (1982).

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  3. W. Drechsler and M. E. Mayer,Fiber Bundle Techniques in Gauge Theories (Lecture Notes in Physics) (Springer-Verlag, Berlin, 1977).

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  4. J. Aczel,Lectures on Functional Equations and Their Applications (Academic, New York, 1966).

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  5. 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.

  6. 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).

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  7. Ibid.,. p. 113.

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  8. Ref. 1,. pp. 691–693.

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  1. ACTA Inc., 24430 Hawthorne Blvd., 90505, Torrance, California

    David Stapleton

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  1. David Stapleton
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Stapleton, D. An application of functional equations to the analysis of the invariance identities of classical gauge field theory. Found Phys 21, 905–929 (1991). https://doi.org/10.1007/BF00733215

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  • DOI: https://doi.org/10.1007/BF00733215

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