Natural Extensions of Electroweak Geometry and Higgs Interactions

2018

Gravit. Cosmol.

Self Cite

We are concerned with the precise modalities by which mathematical constructions related to energy-tensors can be adapted to a tetrad-affine setting. We show that, for fairly general gauge field theories formulated in that setting, two notions of energy tensor-the canonical tensor and the stress-energy tensor-exactly coincide with no need for tweaking. Moreover we show how both notions of energy-tensor can be naturally extended to include the gravitational field itself, represented by a couple constituted by the tetrad and a spinor connection. Then we examine the on-shell divergences of these tensors in relation to the issue of local energy-conservation in the presence of torsion.1 Indeed, a straightforward physical interpretation of the Ricci tensor in terms of energy is problematic as, for example, Schwarzschild spacetime has non-zero gravitational energy while the Ricci tensor vanishes.2 The notion of covariant differential of vector-valued forms, which has been variously present in the literature for several years, is strictly related to the Frölicher-Nijenhuis bracket [38,5,39,40,41]. In this paper we will just write down the needed coordinate expressions.

Section: Introductionmentioning

confidence: 97%

On the Notions of Energy Tensors in Tetrad-Affine Gravity

2018

Gravit. Cosmol.

Self Cite

“…A global soldering form, with the target bundle H constructed from the spinor bundle itself, yields a 'spin structure' on M (in this paper we are not concerned with the possible topological obstructions to the existence of such structures). We also note that the fact that H is explicitely constructed from the spinor bundle is important in the study of gauge field theories coupled with gravity [4,5,6,7,10].…”

Section: Two-spinors and Dirac Spinorsmentioning

confidence: 99%

“…With no loss of generality, the gauge part of the considered connection Γ ′ of U ′ can be completely attributed to a linear Hermitian connection κ of F , leaving the gravitational contribution associated with U only. Even more generally one can assume different 'right' and 'left' Hermitian bundles F R and F L , and define the Fermion bundle to be [7,10]…”

Section: Two-spinors and Dirac Spinorsmentioning

confidence: 99%

“…By contrast, we propose to examine the matter in terms of direct, natural geometric constructions performed by using the fundamental 'building block' constituted by a two-spinor space, that is a 2-dimensional complex vector space endowed with a certain algebraic structure. This approach draws on a partly original treatment of spinors and gauge field theories that has been explored in previous papers [4,5,6,9,10], and is closely related-with differences we won't discuss in detail here-to the Penrose-Reidler 2-spinor formalism [28,29,2]. One then avails of a direct description of higher-rank spinor spaces, and redily grasps the working of the Dirac map and of its extensions to such spaces.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A first-order Lagrangian theory of fields with arbitrary spin

Int. J. Geom. Methods Mod. Phys.

2018

Self Cite

The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic 'building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved spacetime. In particular, one recovers the Bargmann-Wigner equations and the 2(2j + 1)-dimensional representation of the angular-momentum algebra needed for the Joos-Weinberg equations. Looking for a first-order Lagrangian field theory we argue, through considerations related to the 2-spinor description of the Dirac map, that the needed bundle must be a fibered direct sum of a symmetric 'main sector'-carrying an irreducible representation of the angularmomentum algebra-and an induced sequence of 'ghost sectors'. Then one indeed gets a Lagrangian field theory that, at least formally, can be expressed in a way similar to the Dirac theory. In flat spacetime one gets plane-wave solutions that are characterised by their values in the main sector. Besides symmetric spinors, the above procedures can be adapted to anti-symmetric spinors and to Hermitian spinors (the latter describing integer-spin fields). Through natural decompositions, the case of a spin-2 field describing a possible deformation of the spacetime metric can be treated in terms of the previous results.MSC 2010: 81R20, 81R25.

“…One intriguing possibility is that the dilaton be closely related to the Higgs field. My own ideas about such speculations have been expressed in two papers [6,9].…”

Section: Breaking Of Dilaton Symmetrymentioning

confidence: 99%

Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

2018

Arch. Math. (Brno)

Self Cite

An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on "minimal geometric data": all the needed underlying structure is geometrically constructed from the unique assumption of a complex vector field S M with 2-dimensional fibers. The Lie derivatives of objects of all considered types, with respect to a vector field X : M → TM , are well-defined without making any special assumption about X, and fulfill natural mutual relations. MSC 2010: 53B05, 58A32, 83C60. PACS 2010: 02.40.-k, 04.20.Cv.