THEORY OF MOTION FOR MONOPOLE - DIPOLE SINGULARITIES OF CLASSICAL YANG-MILLS HIGGS FIELDS. B. APPROXIMATION SCHEME, EQUATIONS OF MOTION
May, 198359 pages
Published in:
- Phys.Rev.D 29 (1984) 668
Report number:
- MPI-PAE-PTH-3-83
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Abstract: (APS)
In the preceding paper, the laws of motion were established for classical particles with spin which are monopole-dipole singularities of Yang-Mills-Higgs fields. In this paper, a systematic approximation scheme is developed for solving the coupled nonlinear field equations in any order and for determining the corresponding equations of motion. In zeroth order the potentials are taken as the usual Liénard-Wiechert and Bhabha—Harish-Chandra potentials (generalized to isospace); in this order the solutions are necessarily Abelian, since the isovector describing the charge is constant. The regularization necessary to obtain expressions finite on the world lines of the particles is achieved by the method of Riesz potentials. All fields are taken as retarded and are expressed in integral form. Omitting dipole interactions, the integrals for the various terms are carried out as far as possible for general motions, including radiation-reaction terms. In first order, the charge isovectors are no longer necessarily constant; thus the solutions are not necessarily Abelian, and it is possible for charge to be radiated away. The cases of time-symmetric field theory and of an action-at-a-distance formulation of the theory are discussed in an appendix.- GAUGE FIELD THEORY: YANG-MILLS
- MODEL: HIGGS
- FIELD THEORY: CLASSICAL
- POSTULATED PARTICLE: MAGNETIC MONOPOLE
- FIELD EQUATIONS: NONLINEAR
- POTENTIAL
- RENORMALIZATION: REGULARIZATION
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