THE SIGNATURE TRIALITY OF MAJORANA–WEYL SPACE–TIMES

Signature-change events in emergent spacetimes with anisotropic scaling

We investigate the behaviour of quantum fields coupled to a spacetime geometry exhibiting finite regions of Euclidean (Riemannian) signature. Although from a gravity perspective this situation might seem somewhat far fetched, we will demonstrate its direct physical relevance for an explicitly realizable condensed matter system whose linearized perturbations experience an effective emergent spac...

Scalar and spinor fields in signature-changing spacetimes.

The propagation of scalar and spinor fields in a spacetime whose metric changes signature is analyzed. Recent work of Dray et al. on particle production from signature change for a (massless) scalar field is reviewed, and an attempt is made to extend their analysis to the case of a (massless) spin-half field. In contrast to their results for a scalar field, it is shown here—for SL(2, C) spinors...

On an Intriguing Signature-Reversal Exhibited by Cremonian Spacetimes

It is shown that a generic quadro-quartic Cremonian spacetime, which is endowed with one spatial and three time dimensions, can continuously evolve into a signature-reversed configuration, i.e. into the classical spacetime featuring one temporal and three space dimensions. An interesting cosmological implication of this finding is mentioned. In a recent series of papers [1–4], we have introduce...

Hopf Algebras with Triality

In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and ...

Lie Algebras with Triality