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From phase space to multivector matrix m...
Valenzuela, Mauricio...

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From phase space to multivector matrix models by Valenzuela, Mauricio ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
Combining elements of twistor-space, phase space and Clifford algebras, we propose a framework for the construction and quantization of certain (quadric) varieties described by Lorentz-covariant multivector coordiantes. The correspondent multivectors can be parametrized by second order polynomials in the phase space. Thus the multivectors play a double role, as covariant objects in $D=2,3,4 \texttt{ Mod } 8$ space-time dimensions, and as mechanical observables of a non-relativistic system in $2^{[D/2]-1}$ euclidean dimensions. The latter attribute permits a dual interpretation of concepts of non-relativistic mechanics as applying to relativistic space-time geometry. Introducing the Groenewold-Moyal *-product and Wigner distributions in phase space induces Lorentz-covariant non-commutativity and it provides the spectra of geometrical observables. We propose also new (multivector) matrix models, interpreted as descending from the interaction term of a Yang-Mills theory with minimally coupled massive fermions, in the large-$N$ limit, which serves as a physical model containing the constructed multivector (fuzzy) geometries. We also include a section on speculative aspects on a possible cosmological effect and the origin of space-time entropy.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1501.03644
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