Unified Field Theoretical Models from Generalized Affine Geometries

Cirilo-Lombardo, Diego Julio

doi:10.1007/s10773-010-0310-9

Cited by 16 publications

(44 citation statements)

References 17 publications

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“…The model in [4], absolutely consistent from the mathematical and geometrical point of view, was based in a manifold equipped with an underlying hypercomplex structure and zero non-metricity, that lead the important fact that the Torsion of the space-time structure turns to be totally antisymmetric. As is well known in the particular case of totally antisymmetric torsion tensor this type of affine geometrical frameworks have the geodesics and the minimal length equations equivalents.…”

Section: Motivation and Summary Of The Resultsmentioning

confidence: 99%

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Unified Field Theoretical Models from Generalized Affine Geometries II

Cirilo-Lombardo

2011

Int J Theor Phys

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The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288-1301, 2010 is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean (2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the "tratorial" form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.

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Section: Motivation and Summary Of The Resultsmentioning

confidence: 99%

“…Phys. 49:1288-1301, 2010 is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed.…”

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confidence: 99%

Unified Field Theoretical Models from Generalized Affine Geometries II

Cirilo-Lombardo

2011

Int J Theor Phys

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“…As it was shown in [19][20][21][22][23][24] for this model of gravity (see Ref. [25], for astrophysical neutrino applications), the Dirac equation is derived from the same space-time manifold and acquires a coupling modification of the form…”

Section: Introductionmentioning

confidence: 84%

“…As pointed out in references [19][20][21][22][23][24], the torsion vector h = h α dx α (the 4-dimensional dual of the torsion field T βγδ ) plays multiple roles and can be constrained in several different physical situations. Mathematically, it is defined by the Hodge-de Rham decomposition given by the 4-dimensional Helmholtz theorem which states:…”

Section: Generalized Hodge-de Rham Decomposition the Vector Torsmentioning

confidence: 99%

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Fermion Interactions, Cosmological Constant and Space-Time Dimensionality in a Unified Approach Based on Affine Geometry

2014

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One of the main features of unified models, based on affine geometries, is that all possible interactions and fields naturally arise under the same standard. Here, we consider, from the effective Lagrangian of the theory, the torsion induced 4-fermion interaction. In particular, how this interaction affects the cosmological term, supposing that a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early universe. We explicitly show that there is no parity-violating pseudo-scalar density, dual to the curvature tensor (Holst term) and the spinorbilinear scalar density has no mixed couplings of A-V form. On the other hand, the space-time dimensionality cannot be constrained from multidimensional phenomenological models admitting torsion.

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Unified Field Theoretical Models from Generalized Affine Geometries III

Cirilo-Lombardo

2011

Int J Theor Phys

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In this work the underlying structure of new type of Unified Field Theoretical model introduced in by the authors is elucidated and analyzed from the geometrical and group theoretical point of view. Our goal is to take advantage of the geometrical and topological properties of this theory in order to determine the minimal group structure of the resultant spacetime manifold able to support a fermionic structure. From this fact, the relation between antisymmetric torsion and Dirac structure of the spacetime is determined and important physical consequences enumerated. In the case of spacetime with torsion the real meaning of the spin-frame alignment is find and the question of the minimal coupling is discussed based in the important cases of tratorial, totally antisymmetric and general torsion fields. Motivation and Summary of the ResultsAs was pointed out by us in later works [1,2], the cornerstone of the problem of the Unification is where to start conceptually to reformulate the theoretical arena where the Fundamental Theory will be placed, and where the geometry is the unifying essence. According to Mach spacetime doesn't exists without matter. Then, two basic ideas immediately arise to fulfill the observation given by Mach: the concept of dualistic or non-dualistic theories. In the first one the simplest and economical description can be formulated in terms of the gravitational field without torsion plus the energy momentum tensor that, however, is added "by hand" in order to cover the lack of knowledgement of a fundamental structure of the space

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Unified Field Theoretical Models from Generalized Affine Geometries

Cited by 16 publications

References 17 publications

Unified Field Theoretical Models from Generalized Affine Geometries II

Unified Field Theoretical Models from Generalized Affine Geometries II

Fermion Interactions, Cosmological Constant and Space-Time Dimensionality in a Unified Approach Based on Affine Geometry

Unified Field Theoretical Models from Generalized Affine Geometries III

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