Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity

Vacaru, Sergiu I.

doi:10.48550/arxiv.1204.5387

Cited by 1 publication

(7 citation statements)

References 64 publications

(286 reference statements)

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“…Direction 10 is the most important and general one for author's activity during last 20 years. It splits in a number of mutually related sub-directions (see publications [297,299,301,304,305,306,307,308,310,309,314,315,319,321,322,321,325,327,329,335,11,346,350,347,353,355,354,361,356,357,358,362,365,363,366,261,262,371,137,370,138,228,372,139,375,229,240,230,376,…”

Section: B410 Geometric Methods Of Constructing Off-diagonal Solution...mentioning

confidence: 99%

“…(allowing formulation of renormalizable theories and Finsler like theories on Lorentz bundles) were studied in Refs. [355,361,365,371,261,262].…”

Section: B410 Geometric Methods Of Constructing Off-diagonal Solution...mentioning

confidence: 99%

“…There were distinguished such sub-directions of Direction 3 (see publications [284,317,292,289,298,318,299,308,325,343,305,309,361,373]): a) Spinors and Dirac operators on generalized Finsler spaces b) Nonholonomic Clifford structures with nonlinear connections c) Spinors and field interactions in higher order anisotropic spaces.…”

Section: B43 Nonholonomic Clifford Structures and Spinors For Finsler...mentioning

confidence: 99%

“…A series of works (beginning 1995, due to S. Vacaru and co-authors) [284,317,292,289,298,318] were devoted to the geometric definition of locally anisotropic spinors and Dirac operators and elaboration of physical models with Finsler-Lagrange-Hamilton spaces. The monographs [299,308,325] and recent papers [343,305,309,361,373] contain a series of chapters and sections devoted to nonholonomic spinors and twistors and developments for supergravity and noncommutative geometry with applications in modern physics of the so-called nonholonomic Clifford geometry.…”

Section: D) Solutions For Nonholonomic Einstein-dirac Systems and Ext...mentioning

confidence: 99%

“…At present, there is an increasing number of publications with applications in modern engineering, economics etc. For instance, there were published a series of works with fractional derivative diffusion by F. Mainardi (last 30 years) [61] and a reformulation of physical theories on flat spaces to fractional derivatives was proposed by V. E. Tarasov (beginning 2005), see [270,361,356,357] and references therein.…”

Section: B49 Differential Fractional Derivative Geometry Mgts and Def...mentioning

confidence: 99%

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On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles

Vacaru¹

2018

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We develop an axiomatic geometric approach and provide an unconventional review of modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding Lorentz invariance violations, LIVs, classical and quantum random effects, anisotropies etc. There are studied Lorentz-Finsler like theories elaborated as extensions of general relativity, GR, and quantum gravity, QG, models and constructed on (co) tangent Lorentz bundles, i.e. (curved) phase spaces or locally anisotropic spacetimes. An indicator of MDRs is considered as a functional on various type functions depending on phase space coordinates and physical constants. It determines respective generating functions and fundamental physical objects (generalized metrics, connections and nonholonomic frame structures) for relativistic models of Finsler, Lagrange and/or Hamilton spaces. We show that there are canonical almost symplectic differential forms and adapted (non) linear connections which allow us to formulate equivalent almost Kähler-Lagrange / -Hamilton geometries. This way, it is possible to unify geometrically various classes of (non) commutative MGTs with locally anisotropic gravitational, scalar, non-Abelian gauge field, and Higgs interactions. We elaborate on theories with Lagrangian densities containing massive graviton terms and bi-connection and bi-metric modifications which can be modelled as Finsler-Lagrange-Hamilton geometries. An example of short-range locally anisotropic gravity on (co) tangent Lorentz bundles is analysed. We conclude that a large class of such MGTs admits a self-consistent causal axiomatic formulation which is similar to GR but involving generalized (non) linear connections, Finsler metrics and adapted frames on phase spaces. Such extensions of the standard model of particle physics and gravity offer a comprehensive guide to classical formulation of MGTs with MDRs, their quantization, applications in modern astrophysics and cosmology, and search for observable phenomena and experimental verifications. An appendix contains historical remarks on elaborating Finsler MGTs and a summary of author's results in twenty directions of research on (non) commutative/ supersymmetric Finsler geometry and gravity; nonholonomic geometric flows, locally anisotropic superstrings and cosmology, etc.

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Section: B410 Geometric Methods Of Constructing Off-diagonal Solution...mentioning

confidence: 99%

“…(allowing formulation of renormalizable theories and Finsler like theories on Lorentz bundles) were studied in Refs. [355,361,365,371,261,262].…”

Section: B410 Geometric Methods Of Constructing Off-diagonal Solution...mentioning

confidence: 99%

Section: B43 Nonholonomic Clifford Structures and Spinors For Finsler...mentioning

confidence: 99%

Section: D) Solutions For Nonholonomic Einstein-dirac Systems and Ext...mentioning

confidence: 99%

Section: B49 Differential Fractional Derivative Geometry Mgts and Def...mentioning

confidence: 99%

See 3 more Smart Citations

On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles

Vacaru¹

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity

Cited by 1 publication

References 64 publications

On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles

On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles

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