Results 1 to 10 of about 167 (143)
The standard model, the Pati–Salam model, and ‘Jordan geometry’
New Journal of Physics, 2020 We argue that the ordinary commutative and associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algebra (as in noncommutative geometry), but rather by a Jordan algebra ...
Latham Boyle, Shane Farnsworth
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Quantum Riemannian geometry of phase space and nonassociativity
Demonstratio Mathematica, 2017 Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and Riemannian ...
Beggs Edwin J., Majid Shahn
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Noncommutative Differential Geometry of Generalized Weyl Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2016 Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed.
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Some special types of determinants in graded skew P BW extensions.
Revista Integración, 2021 In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslanderregular algebra has trivial homological determinant.
Héctor Suárez +2 more
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Noncommutative scalar fields: Quantum symmetries and braided BV quantization [PDF]
Kragujevac Journal of ScienceIt is strongly believed that the fully consistent quantum gravity theory should lead to a quantum spacetime. The continuous description of spacetime in terms of differential manifolds is no longer adequate at the quantum gravity energies.
Bežanić Milorad +2 more
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AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS [PDF]
International Journal of Modern Physics A, 1993 We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q→1 limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan-Maurer equations is presented.
Aschieri, Paolo, Castellani, Leonardo
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A new algebraic structure in the standard model of particle physics
Journal of High Energy Physics, 2018 We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to
Latham Boyle, Shane Farnsworth
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Noncommutative differential geometry with higher-order derivatives [PDF]
Letters in Mathematical Physics, 1994 We build a toy model of differential geometry on the real line, which includes derivatives of the second order. Such construction is possible only within the framework of noncommutative geometry. We introduce the metric and briefly discuss two simple physical models of scalar field theory and gauge theory in this geometry.
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Field Theory on Curved Noncommutative Spacetimes
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by using (
Alexander Schenkel +1 more
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Deformation quantization and intrinsic noncommutative differential geometry
, 2023 We provide an intrinsic formulation of the noncommutative differential geometry developed earlier by Chaichian, Tureanu, R. B. Zhang and the second author. This yields geometric definitions of covariant derivatives of noncommutative metrics and curvatures, as well as the noncommutative version of the first and the second Bianchi identities.
Gao, Haoyuan, Zhang, Xiao
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