English

Exploring the Causal Structures of Almost Commutative Geometries

Mathematical Physics 2014-01-29 v2 General Relativity and Quantum Cosmology math.MP Operator Algebras

Abstract

We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra S(R1,1)M2(C)\mathcal{S}(\mathbb{R}^{1,1}) \otimes M_2(\mathbb{C}), which has a non-trivial space of internal degrees of freedom. It turns out that the causality condition imposes restrictions on the motion in the internal space. Moreover, we show that the requirement of causality favours a unitary evolution in the internal space.

Keywords

Cite

@article{arxiv.1310.8225,
  title  = {Exploring the Causal Structures of Almost Commutative Geometries},
  author = {Nicolas Franco and Michał Eckstein},
  journal= {arXiv preprint arXiv:1310.8225},
  year   = {2014}
}
R2 v1 2026-06-22T01:57:37.206Z