Physics – Classical Physics
Scientific paper
2000-12-08
International Journal of Mathematics and Mathematical Sciences, 31 (2002) 149-155
Physics
Classical Physics
6 pages, LaTeX, Poster at the XXIII International Colloquium on Group Theoretical Methods in Physics, July 31 - August 5, JINR
Scientific paper
By symmetry of the partial differential equation L'\phi'(x')=0 with respect to the variables replacement x'=x'(x), \phi'=\phi'(\Phi\phi) it is advanced to understand the compatibility of engaging equations system A\phi'(\Phi\phi)=0, L\phi(x)=0, where A\phi'(\Phi\phi)=0 is obtained from the initial equation by replacing the variables, L'=L, \Phi(x) is some weight function. If the equation A\phi'(\Phi\phi)=0 may be transformed to the form L(\Psi\phi)=0, where \Psi(x) is the weight function, the symmetry will be named the standard Lie symmetry, otherwise the generalized symmetry. It is shown that with the given understanding of the symmetry, D'Alembert equation for one component field is invariant with respect to any arbitrary reversible coordinate transformations x'=x'(x). In particular, they contain the transformations of the conformal and Galilei groups realizing the type of standard and generalized symmetry for \Phi(x)=\phi'(x'\to x)/\phi(x).
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