On invariance functions in Relativity Theory
Abstract
A new result for equivariant functions in terms of invariant functions in the case of Minkowski space is given. This generalizes the work of Hall and Wightman in the sense that only equivariance is required. In particular, it implies the possibility of defining physical magnitudes independently of the choice of the coordinate system, like the center of mass for relativistic particles.
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I. M. Gelfand, R. A. Minlos, and Z. Ya. Shapiro. Representations of the Rotation and Lorentz groups and their Applications. Pergamon, London; Macmillan, New York, 1963.
D. Hall and A. S. Wightman. A Theorem on Invariant Analytic Functions with Applications to Relativistic Quantum Field Theory, E. Munksgaard, publisher. 1957.
M. A. Naimark. Linear Representations of the Lorentz Group, (International Series of Monographs in Pure and Applied Mathematics, Vol. 63) Oxford/London/Edinburgh/New York/Paris/Frankfurt. Pergamon Press, 1964.
Y. Matsushima. Differentiable Manifolds, (Series in Pure and Applied Mathematics, Vol 9) New York Basel. Macel Dekker, Inc., 1972.
A. Pli, T. Zastawniak. Relativistic Quantum Mechanics for two interacting particles in one-time representation. Reports on Mathematical Physics, 31, 317(1992).
E. Hewitt, K. A. Ross. Abstract Harmonic Analysis I. Grundlehren der mathematischen Wissenchaften 115. Springer Verlag New York, Inc. 2nd Edition, 1979.
A. Wawrzyczyk. Group Representations and Special Functions. D. Reidel Publishing Company. Mathematics and Its Applications (East European Series). Dordrecht-Boston-Lancaster, 1984.
M. Reisert, H. Burkhardt. Learning Equivariant Functions with Matrix Valued Kernels. Journal of Machine Learning Research 8, 305(2007).
A. Sebbar, A. Sebbar. Equivariant functions and integrals of elliptic functions. Geometriae Dedicata, 160, 373(2012).
A. G. Wasserman. Equivariant Differential Topology. Topology, 8, 127(1969).
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