2016/11/21 by Nadir Bizi, Bizi, Nadir, Christian Brouder +3 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1611.07062
openalex publication_date 2016/11/21 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
An analogy with real Clifford algebras on even-dimensional vector spaces\nsuggests to assign a couple of space and time dimensions modulo 8 to any\nalgebra (represented over a complex Hilbert space) containing two self-adjoint\ninvolutions and an anti-unitary operator with specific commutation relations.\n It is shown that this assignment is compatible with the tensor product: the\nspace and time dimensions of the tensor product are the sums of the space and\ntime dimensions of its factors. This could provide an interpretation of the\npresence of such algebras in PT-symmetric Hamiltonians or the description of\ntopological matter.\n This construction is used to build an indefinite (i.e. pseudo-Riemannian)\nversion of the spectral triples of noncommutative geometry, defined over Krein\nspaces instead of Hilbert spaces. Within this framework, we can express the\nLagrangian (both bosonic and fermionic) of a Lorentzian almost-commutative\nspectral triple. We exhibit a space of physical states that solves the\nfermion-doubling problem. The example of quantum electrodynamics is described.\n