Geometrical aspects in Yang–Mills gauge theories

Cianci, Roberto; Vignolo, Stefano; Bruno, Danilo

doi:10.1088/0305-4470/37/6/040

Cited by 12 publications

(37 citation statements)

References 3 publications

(22 reference statements)

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“…J -bundles have been recently used to provide new geometric formulations of gauge theories and GR [1][2][3][29][30][31][32].…”

Section: The Geometric Frameworkmentioning

confidence: 99%

“…The geometry of J -bundles has been thoroughly examined in Refs. [1][2][3]. As a matter of fact, the quotient projection ρ endows the bundle J (E × C) with most of the standard features of jet-bundles geometry (J -extension of sections, contact forms, J -prolongation of morphisms and vector fields), which are needed to implement variational calculus on J (E × C).…”

Section: The Geometric Frameworkmentioning

confidence: 99%

“…Referring the readers to [1][2][3] for a detailed discussion on J -bundles geometry, the relevant fact we need to recall here is that the components of the torsion and curvature tensors can be chosen as fiber J -coordinates on J (E × C). In fact, the following relations…”

Section: The Geometric Frameworkmentioning

confidence: 99%

“…In some previous papers [1][2][3], a new geometric approach for Gauge Theories and General Relativity (GR), in the tetrad-affine formulation, has been proposed. It is called the J -bundles framework (from now on the J -bundles).…”

Section: Introductionmentioning

confidence: 99%

“…In view of this fact, the basic idea developed in [1][2][3] consists of defining a suitable quotient space of the first jet-bundle, making equivalent two sections which have a first order contact with respect to the exterior differentiation (or, equivalently, with respect to the exterior covariant differentiation), instead of the whole set of derivatives. The resulting fiber coordinates of the so defined new spaces are exactly the antisymmetric combinations appearing in the Lagrangian densities.…”

Section: Introductionmentioning

confidence: 99%

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f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

Capozziello

Cianci

Stornaiolo

et al. 2008

Int. J. Geom. Methods Mod. Phys.

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We discuss the f (R)-theories of gravity with torsion in the framework of J -bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber J -coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f (R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang-Mills fields and spin perfect fluid. Such fields enlarge the jet bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f (R)-gravity and scalar-tensor theories.

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“…J -bundles have been recently used to provide new geometric formulations of gauge theories and GR [1][2][3][29][30][31][32].…”

Section: The Geometric Frameworkmentioning

confidence: 99%

Section: The Geometric Frameworkmentioning

confidence: 99%

Section: The Geometric Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

Capozziello

Cianci

Stornaiolo

et al. 2008

Int. J. Geom. Methods Mod. Phys.

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A square‐torsion modification of Einstein‐Cartan theory

2012

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In the present paper we consider a theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant. In particular, we discuss the couplings to Dirac fields and spin fluids: in the case of Dirac fields, we discuss how in our approach, the Dirac self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales, showing different applications according to the value of the parameter we have assigned; in the case of spin fluids, we discuss FLRW cosmological models arising from the proposed theory

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Extended Theories of Gravity

2011

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Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is aimed to address conceptual and experimental problems recently emerged in Astrophysics, Cosmology and High Energy Physics. In particular, the goal is to encompass, in a self-consistent scheme, problems like Inflation, Dark Energy, Dark Matter, Large Scale Structure and, first of all, to give at least an effective description of Quantum Gravity. We review the basic principles that any gravitational theory has to follow. The geometrical interpretation is discussed in a broad perspective in order to highlight the basic assumptions of General Relativity and its possible extensions in the general framework of gauge theories. Principles of such modifications are presented, focusing on specific classes of theories like f (R)-gravity and scalar-tensor gravity in the metric and Palatini approaches. The special role of torsion is also discussed. The conceptual features of these theories are fully explored and attention is payed to the issues of dynamical and conformal equivalence between them considering also the initial value problem. A number of viability criteria are presented considering the post-Newtonian and the post-Minkowskian limits. In particular, we discuss the problems of neutrino oscillations and gravitational waves in Extended Gravity. Finally, future perspectives of Extended Gravity are considered with possibility to go beyond a trial and error approach.Comment: 184 pages, 3 figures, survey to appear in Physics Report

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Geometrical aspects in Yang–Mills gauge theories

Abstract: A gauge-independent formulation of the theory developed in J. Phys. A: Math. Gen. 36 8341 ( 2003) is proposed.

Cited by 12 publications

References 3 publications

f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

f(R) GRAVITY WITH TORSION: A GEOMETRIC APPROACH WITHIN THE $\mathcal{J}$-BUNDLES FRAMEWORK

A square‐torsion modification of Einstein‐Cartan theory

Extended Theories of Gravity

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