Group theory and solutions of classical field theories with polynomial nonlinearities |
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Authors: | A M Grundland J A Tuszyński P Winternitz |
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Institution: | (1) Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128-A, H3C 3J7 Montréal, QC, Canada;(2) Department of Physics, University of Alberta, T6G 2J1 Edmonton, Alberta, Canada |
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Abstract: | In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical 4 and 6 field theory, the former with and without the inclusion of an external force field conjugate to . Both massive (m0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the 4 model and demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both 4 and 6 cases since they provide the most realistic models of elementary particles. |
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