Time-reversal properties in the coupling of quantum angular momenta

TL;DR

This paper explores the role of time-reversal symmetry in quantum angular momentum coupling, challenging existing superselection rules and analyzing hidden symmetries like SO(4) in systems with Keplerian dynamics.

Contribution

It demonstrates the redundancy of the double time-reversal superselection rule and clarifies how hidden symmetries affect Wigner's theorem in angular momentum coupling.

Findings

Double time-reversal superselection rule is redundant.

Hidden SO(4) symmetry influences angular momentum coupling.

Wigner's theorem limitations in presence of hidden symmetries.

Abstract

After a synoptic panorama about some still unsolved foundational problems involving time-reversal, we show that the \emph{double time-reversal superselection rule} of Nonrelativistic Quantum Mechanics is redundant. We then analyze which, among the symmetries of the Clebsch-Gordan coefficients, may be inferred through time-reversal considerations. Finally, we show how Coupling Theory allows to improve our comprehension of the fact that, in presence of hidden symmetries, Wigner's Theorem concerning Kramers degeneration cannot be applied, by analyzing a set of Z uncoupled massive particles, both in the case in which they are bosons of spin zero and in the case in which they are fermions of spin 1/2, subjected to a Keplerian force's field and considering the coupling of the 2Z quantum angular momenta resulting by the hidden SO(4) symmetry owed to the fact that, apart from the rotational SO(3) symmetry responsible of the conservation of the angular momentum, the Laplace-Runge-Lenz vector is also conserved.