The super-Poincaré algebra via pure spinors and the interaction principle in 3D Euclidean space

Rocha, Roldão da

doi:10.1590/s0103-97332005000700035

Cited by 2 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [1] it was proved that new deformed octonionic units with respect to the nonassociative product between Clifford bundle sections and octonionic fields can be introduced, in order to better investigate the generalization of Moufang identities in this context. Using the formalism presented and its generalization [20,21], the Poincaré superalgebra is obtained from the Clifford orthosymplectic algebra [21]. It was also shown in [20] -following [21] that the Chevalley product, an order three automorphism on the vector space constructed as the direct sum of maximal index vector spaces and their semispinor associated spaces, induces triality like morphisms on some subspaces of the associated complexified exterior algebra.…”

Section: Introductionmentioning

confidence: 99%

“…Using the formalism presented and its generalization [20,21], the Poincaré superalgebra is obtained from the Clifford orthosymplectic algebra [21]. It was also shown in [20] -following [21] that the Chevalley product, an order three automorphism on the vector space constructed as the direct sum of maximal index vector spaces and their semispinor associated spaces, induces triality like morphisms on some subspaces of the associated complexified exterior algebra. See [22] for details including historical notes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized non-associative structures on the 7-sphere

Rocha

Traesel

2012

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

In this paper we provide a more general class of non-associative products using the exterior and Clifford bundles on the 7-sphere S 7 . Some additional properties encompass the previous formalisms presented in [1,2] in the Clifford algebra context, and wider classes of non-associative structures on S 7 are investigated, evinced by the directional non-associative products and the mixed composition of generalized non-associative products between Clifford algebra multivectors. These non-associative products are further generalized by considering the non-associative shear of arbitrary Clifford bundle Cℓ0,7 elements into octonions. We assert new properties inherited from the non-associative structure introduced in the whole Clifford bundle on S 7 , which naturally induce involutions on the Clifford bundle and provide immediate generalizations concerning well-established formal results in, e.g., [3,4,5,6,7] and potential applications in physics as pioneered by, e. g., [2,3,4,5,6,7,8,9,10,11,12,13,14].

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized non-associative structures on the 7-sphere

Rocha

Traesel

2012

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

Elko Spinor Fields: Lagrangians for Gravity Derived From Supergravity

Rocha

Silva

2009

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belongtogether with Majorana spinor fields -to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the EinsteinPalatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that -in particular -the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator -leading ELKO Lagrangian into the Dirac Lagrangian -is also pointed out, together with its relationship to the instanton Hopf fibration.

show abstract

The super-Poincaré algebra via pure spinors and the interaction principle in 3D Euclidean space

Cited by 2 publications

References 7 publications

Generalized non-associative structures on the 7-sphere

Generalized non-associative structures on the 7-sphere

Elko Spinor Fields: Lagrangians for Gravity Derived From Supergravity

Contact Info

Product

Resources

About