Hints of a new relativity principle from p-brane quantum mechanics

Castro, Carlos

doi:10.1016/s0960-0779(00)00019-9

Cited by 30 publications

(32 citation statements)

References 32 publications

(113 reference statements)

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“…Applications of Clifford algebras methods in general relativity appeared also, e.g., in [35,90,54,55,57,58,62,103,104,105,119,134,154], and suggest new ways for looking to the gravitational field. Clifford algebras methods, have been applied successfully also in quantum field theory, as , e.g., in [60,138] and more recently in string and p-brane theories, with noticeable results ( [25]- [34], [136,137]) which are worth to be more carefully investigated.…”

Section: Introductionmentioning

confidence: 99%

Algebraic and Dirac–Hestenes spinors and spinor fields

Rodrigues

2004

Journal of Mathematical Physics

122

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Almost all presentations of Dirac theory in first or second quantization in Physics (and Mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of non homogeneous even multivectors fields) is used. However, a carefully analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF ) and Dirac-Hestenes spinor fields (DHSF ) on Minkowski spacetime as some equivalence classes of pairs (Ξu, ψ Ξu ), where Ξu is a spinorial frame field and ψ Ξu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a carefull analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the 'bilinear covariants' (on Minkowski spacetime) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary RiemannCartan spacetimes. The present paper contains also Appendices (A-E) which exhibits a truly useful collection of results concerning the theory of

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Section: Introductionmentioning

confidence: 99%

Algebraic and Dirac–Hestenes spinors and spinor fields

Rodrigues

2004

Journal of Mathematical Physics

122

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“…Recently we have proposed that a New Relativity principle may be operating in Nature which could reveal important clues to find the origins of M theory [1]. We were forced to introduce this New Relativity principle, where all dimensions and signatures of spacetime are on the same footing, to find a fully covariant formulation of the p-brane Quantum Mechanical Loop Wave equations.…”

Section: Historical Backgroundmentioning

confidence: 99%

“…Before we begin the present status and prsopects of the New Relativity Theory [1] we deem it very important to review in 1 the New Extended Scale Relativity and its postulates. This is all one needs to construct in 2 the generalization of the Quenched-Minisuperspace bosonic p-brane propagator in D dimensions [18] ; i.e the Multidimensional-Particle propagator in C-spaces ( Clifford ) associated with a nested family of p-loop histories living in a D-dimensional target spacetime background.…”

Section: Introduction : the New Relativity Theorymentioning

confidence: 99%

The status and programs of scale relativity theory

Castro

2001

Chaos, Solitons & Fractals

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A review of the most recent results of the New Relativity Theory is presented. These include a straightforward derivation of the Black Hole Entropy-Area relation and its logarithmic corrections; the derivation of the string uncertainty relations and generalizations ; ; the relation between the four dimensional gravitational conformal anomaly and the fine structure constant; the role of Noncommutative Geometry, Negative Probabilities and Cantorian-Fractal spacetime in the Young's two-slit experiment. We then generalize the recent construction of the Quenched-Minisuperspace bosonic p-brane propagator in D dimensions (AACS [18] ) to the full multidimensional case involving all p-branes : the construction of the Multidimensional-Particle propagator in Clifford spaces ( C-spaces ) associated with a nested family of p-loop histories living in a target D-dim background spacetime . We show how the effective C-space geometry is related to extrinsic curvature of ordinary spacetime. The motion of rigid particles/branes is studied to explain the natural emergence of classical spin. The relation among C-space geometry and W, Finsler Geometry and ( Braided ) Quantum Groups is discussed. Some final remarks about the Riemannian long distance limit of C-space geometry are made.

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“…The stringy corrections to the original Heisenberg's uncertainty principle also follow directly from the quantum mechanical wave equations on noncommutative Clifford manifolds where all dimensions and signatures of spacetime are on the same footing [26]. Castro has considered the new relativity principle to find a fully covariant formulation of the p-brane quantum mechanical loop wave equations where the string uncertainty relations arrises naturally.…”

Section: Introductionmentioning

confidence: 99%

“…This is an inherent noncommutative nature of the Clifford manifold which reshuffles a loop history into a membrane history, a membrane history into a p-brane history or more generally it can transform a p-brane history into suitable combinations of the other p-brane histories as building blocks. This bootstrap idea is taken from the point particle case to the p-branes case with each brane made out of all the other p-branes where the Lorentz transformations in C-spaces involve hypermatrix changes of coordinates in the p-brane quantum mechanics [26].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Uncertainty Principle

Crowell¹

2005

World Scientific Series in Contemporary Chemical Physics

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We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation to analyze the quantum theory of gravity or string theory from the perspective of a complex function. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent functionδ(∆x, ∆k, ǫ). We arrived at the string uncertainty principle from the analyticity condition of a newly introduced complex function which depends upon the UV cut-off. This non trivially modifies the quantum measurements, black hole physics and short distance geometries. Present analysis is based on the postulate that the Planck scale is the minimal length scale in nature and is in good agreement with the existance of maximum length scale in the nature. Both of these rely only on the analysis of the complex function and do not directly make use of any theory or the specific structure of the Hamiltonian. The Regge behaviour of the string spectrum with the quantization of area is also a natural consequence of our new complex function which may contain all the corrections operating in nature and reveal important clues to find the origins of the M-theory.

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Hints of a new relativity principle from p-brane quantum mechanics

Cited by 30 publications

References 32 publications

Algebraic and Dirac–Hestenes spinors and spinor fields

Algebraic and Dirac–Hestenes spinors and spinor fields

The status and programs of scale relativity theory

The Generalized Uncertainty Principle

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