An introduction to nonassociative physics

Szabo, Richard J.

doi:10.22323/1.347.0100

Cited by 15 publications

(29 citation statements)

References 160 publications

(272 reference statements)

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“…In above formulas, the nonassociative metric compatibility of both linear connections is stated as in (30) and the star canonical s-torsion components are parameterized following decompositions(A.8), when…”

Section: Star Deformed Lc-connections and Canonical S-connectionsmentioning

confidence: 99%

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Decoupling and Integrability of Nonassociative Vacuum Phase Space Gravitational Equations With Star and R‐flux Parametric Deformations

Veliev

Bubuianu²,

Vacaru

2021

Fortschritte der Physik

113

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We prove that nonassociative star deformed vacuum Einstein equations can be decoupled and integrated in certain general forms on phase spaces involving real R-flux terms induced as parametric corrections on base Lorentz manifold spacetimes. The geometric constructions are elaborated with parametric (on respective Planck, ℏ, and string, := 3 s ∕6ℏ, constants) and nonholonomic dyadic decompositions of fundamental geometric and physical objects. This is our second partner work on elaborating nonassociative geometric and gravity theories with symmetric and nonsymmetric metrics, (non) linear connections, star deformations defined by generalized Moyal-Weyl products, endowed with quasi-Hopf algebra, or other type algebraic and geometric structures, and all adapted to nonholonomic distributions and frames. We construct exact and parametric solutions for nonassociative vacuum configurations (with nontrivial or effective cosmological constants) defined by star deformed generic off-diagonal (non) symmetric metrics and (generalized) nonlinear and linear connections. The coefficients of geometric objects defining such solutions are determined by respective classes of generating and integration functions and constants and may depend on all phase space coordinates [spacetime ones, (x i , t); and momentum like variables, (p a , E)]. Quasi-stationary configurations are stated by solutions with spacetime Killing symmetry on a time like vector t but with possible dependencies on momentum like coordinates on star deformed phase spaces. This geometric techniques of decoupling and integrating nonlinear systems of physically important partial differential equations (the anholonomic frame and connection deformation method, AFCDM) is applied in our partner works for constructing nonassociative and locally anisotropic generalizations of black hole and cosmological solutions and elaborating geometric flow evolution and classical and quantum information theories.

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Section: Star Deformed Lc-connections and Canonical S-connectionsmentioning

confidence: 99%

“…It should be noted that algebras and geometries with nonassociative structure arise from various developments on quantum mechanics with magnetic monopole, string and M-theory with non-geometric fluxes etc., see [28][29][30] for reviews of such approaches.…”

Section: Introductionmentioning

confidence: 99%

Decoupling and Integrability of Nonassociative Vacuum Phase Space Gravitational Equations With Star and R‐flux Parametric Deformations

Veliev

Bubuianu²,

Vacaru

2021

Fortschritte der Physik

113

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“…Another approach is to enlarge the phase space for the electric charge, and this was done recently by Kupriyanov and Szabo [1]. The result has implications for certain nongeometric string theories and their quantization, which leads to nonassociative algebras, see e.g., [5]- [13].…”

Section: Introductionmentioning

confidence: 99%

Lagrangian formulation for electric charge in a magnetic monopole distribution

Marmo¹,

Scardapane²,

Stern

et al. 2019

Phys. Rev. D

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We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the nonrelativistic Lagrangian agrees with the Hamiltonian description given recently by Kupriyanov and Szabo [1]. The covariant relativistic version of the Lagrangian is shown to introduce a new gauge symmetry, in addition to standard reparametrizations. The generalization of the system to open strings coupled to a magnetic monopole distribution is also given, as well as the generalization to particles in a non-Abelian gauge field which does not satisfy Bianchi identities in some region of the space-time. *

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“…Nonassociative algebras play a significant role in physics. An introduction to nonassociative physics is given in [], and recent developments are presented in []. An elementary example of a nonassociative algebra is a Lie algebra.…”

Section: Introductionmentioning

confidence: 99%

“…However, a Lie algebra is too restrictive in some systems. For instance, it is known that other nonassociative algebras appear in quantum mechanics with magnetic monopoles, string theory, and M‐theory …”

Section: Introductionmentioning

confidence: 99%