A class of nonlinear realizations of the poincare group
19728 pages
Published in:
- J.Math.Phys. 13 (1972) 275-282
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Abstract: (AIP)
A class of nonlinear space‐time transformations is exhibited, which forms a nonlinear realization of the Poincaré group. The transformations leave the expression I = x 2+f(x μ/x 0) invariant; f is an arbitrary function of the ratios x μ/x 0. The infinitesimal generators are constructed as differential operators in the Minkowski space. The transformations are defined only in a restricted region A (the allowed region) of the Minkowski space. By introducing auxiliary variables, the transformations can be recast in their usual linear form; this, however, is in general possible only in a region L (the linear region) which is different from A . The region structure is analyzed in general and given explicitly for a special form of the function f. Among the physical ideas suggested by the nonlinear formalism is the notion of ``relativity of coincidence.'' This expresses the fact that events coincident (or having arbitrary small Minkowski separation) in one frame of reference will not be coincident (or will have finite Minkowski separation) in a transformed frame.- group theory: lorentz
- transformation
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