States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution [PDF]
, 2014 A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and semiclassical equations,
Bojowald, Martin +3 more
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Particle models from special Jordan backgrounds and spectral triples [PDF]
, 2022 We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for general, almost ...
Besnard, F., Farnsworth, S.
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Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories [PDF]
, 1996 In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories (fermion ...
A. Chamseddine +12 more
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Cosmological perturbations and short distance physics from Noncommutative Geometry [PDF]
, 2002 We investigate the possible effects on the evolution of perturbations in the inflationary epoch due to short distance physics. We introduce a suitable non local action for the inflaton field, suggested by Noncommutative Geometry, and obtained by adopting
A. Connes +33 more
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Spectra of observables in the q-oscillator and q-analogue of the Fourier transform [PDF]
, 2005 Spectra of the position and momentum operators of the Biedenharn-Macfarlane q-oscillator (with the main relation aa^+-qa^+a=1) are studied when q>1. These operators are symmetric but not self-adjoint.
Klimyk, Anatoliy
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A Dark Sector Extension of the Almost-Commutative Standard Model [PDF]
, 2013 We consider an extension of the Standard Model within the frame work of Noncommutative Geometry. The model is based on an older model [St09] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which
Stephan, Christoph A.
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Position-dependent noncommutative products: classical construction and field theory [PDF]
, 2005 We look in Euclidean $R^4$ for associative star products realizing the commutation relation $[x^\mu,x^\nu]=i\Theta^{\mu\nu}(x)$, where the noncommutativity parameters $\Theta^{\mu\nu}$ depend on the position coordinates $x$.
Araki +45 more
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Studies on A. Einstein , B. Podolsky and N. Rosen argument that ”quantum mechanics is not a complete theory,” I: Basic methods [PDF]
, 2020 In 1935, A. Einstein expressed his view, jointly with B. Podolsky and N. Rosen, that ”quantum mechanics is not a complete theory” (EPR argument). Following decades of preparatory studies, R. M.
Santilli, Ruggero Maria
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Dynamical Correspondence in a Generalized Quantum Theory
, 2015 In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras).
Niestegge, Gerd
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Noncommutative Geometries and Gravity
, 2007 We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.Comment: 18 pages, to appear in the Proceedings of the Third Mexican Meeting on Mathematical and Experimental Physics, Symposium on
Abel Camacho +3 more
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