A general mathematical structure for the time-reversal operator
Abstract
The aim of this work is the mathematical analysis of the physical time-reversal operator and its definition as a geometrical structurebf, in such a way that it could be generalized to the purely mathematical realm. Rigorously, only having such a ``time-reversal structure'' it can be decided whether a dynamical system is time-symmetric or not.it\The ``time-reversal structures'' of several important physical and mathematical examples are presented, showing that there are some mathematical categories whose objects are the (classical or abstract) ``time-reversal systems'' and whose morphisms generalize the Wigner transformation.
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