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A general mathematical structure for the time-reversal operator

Mario Alberto Castagnino·Adolfo Ramon Ordoniez·Daniela Beatriz Emmanuele
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Abstract

The aim of this work is the mathematical analysis of the physical time-reversal operator and its definition as a geometrical structure\QTR{bf}{, }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.\QTR{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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Mario Alberto Castagnino, Adolfo Ramon Ordoniez, Daniela Beatriz Emmanuele. 2001-03-23. A general mathematical structure for the time-reversal operator. https://arxiv.org/abs/quant-ph/0103132

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