Non-relativistic Space–Time Symmetries

Michael E. Kellman

It is argued that the standard quantum mechanical description of the Bell correlations between entangled subsystems is in conflict with relativistic space-time symmetry. Proposals to abandon relativistic symmetry, in the sense of explicitly returning to an absolute time and preferred frame, are rejected on the grounds that the preferred frame is not empirically detectable, so the asymmetry is an unsatisfactory feature in physical theory. A "symmetric view" is proposed in which measurement events on space-like separated entangled subsystems are connected by a symmetric two-way mutual influence. Because of this reciprocity, there is complete symmetry of the description: Einsteinian relativity of simultaneity and space-time symmetry are completely preserved. The nature of the two-way influence is considered, as well as the possibility of an empirical test.

Florian A. Scheck

Minoru Omote, S. Kamefuchi

On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.

UMBERTO LOMBARDO, G. Giuliani, Yifei Niu

Jyong-Hao Chen, Christopher Mudry, Claudio Chamon +1 more

We study a model in (2 + 1)-dimensional space-time that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1 + 1)-dimensional space-time, coupled via current-current interactions. The model is shown to have a lattice realization as an array of coupled quantum spin-1/2 ladders. We study this model both in the presence and in the absence of time-reversal symmetry within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin-liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime for which a nonchiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2 + 1)-dimensional space-time, much as those appearing in the Kitaev honeycomb model but here emerging in a model of coupled spin ladders that do not break the $SU(2)$ spin-rotation symmetry.