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On the relationship between conservation laws and invariance groups of nonlinear field equations in Hamilton's canonical form
It is shown that whenever fields governed by the equations /tp=−H/q, /tq =H/p allow a conservation law of the form /t+divJ=0, there exists a corresponding Lie–Bäcklund infinitesimal c...
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Symmetries in gauge theories
A general definition of symmetry for solutions of the field equations of gauge theories is proposed, and some of its properties and consequences are discussed.

Symmetry and separation of variables for the Hamilton–Jacobi equation W<sup>2</sup><sub>t</sub>−W<sup>2</sup><sub>x</sub> −W<sup>2</sup><sub>y</sub> =0

J. Math. Phys. 19, 200 (1978); doi:10.1063/1.523539

Issue Date: January 1978

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C. P. Boyer, E. G. Kalnins, and W. Miller, Jr.
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México 20, D. F., Mexico
Mathematics Department, University of Waikato, Hamilton, New Zealand
School of Mathematics, University of Minnesota, Minneapolis, Minnesota
We present a detailed group theoretical study of the problem of separation of variables for the characteristic equation of the wave equation in one time and two space dimensions. Using the well-known Lie algebra isomorphism between canonical vector fields under the Lie bracket operation and functions (modulo constants) under Poisson brackets, we associate, with each R-separable coordinate system of the equation, an orbit of commuting constants of the motion which are quadratic members of the universal enveloping algebra of the symmetry algebra o (3,2). In this, the first of two papers, we essentially restrict ourselves to those orbits where one of the constants of the motion can be split off, giving rise to a reduced equation with a nontrivial symmetry algebra. Our analysis includes several of the better known two-body problems, including the harmonic oscillator and Kepler problems, as special cases. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
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PACS

  • 02.30.Jr
    Mathematical methods in physics Function theory, analysis Partial differential equations
  • YEAR: 1978

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ISSN:
0022-2488 (print)   1089-7658 (online)
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