arXiv subjects

William M. Pezzaglia

Publications and source records attributed to William M. Pezzaglia.

5 recordsLinked to original sources

arXiv1999

Dimensionally Democratic Calculus and Principles of Polydimensional Physics

A solution to the 50 year old problem of a spinning particle in curved space has been recently derived using an extension of Clifford calculus in which each geometric element has its own coordinate. This leads us to propose that all the laws of physics should obey new polydimensional metaprinciples, for which Clifford algebra is the natural language of expression, just as tensors were for general relativity. Specifically, phenomena and physical laws should be invariant under local automorphism transformations which reshuffle the physical geometry. This leads to a new generalized unified basis for classical mechanics, which includes string theory, membrane theory and the hypergravity formulation of Crawford[J. Math. Phys., {\bf 35}, 2701-2718 (1994)]. Most important is that the broad themes presented can be exploited by nearly everyone in the field as a framework to generalize both the Clifford calculus and multivector physics.

gr-qc↗

arXiv1999

Polydimensional Supersymmetric Principles

Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus in which each geometric element (vector, bivector) has its own coordinate. A new classical action principle is proposed in which particles take paths which minimize the distance traveled plus area swept out by the spin. This leads to a solution of the 50 year old conundrum of `what is the correct Lagrangian' in which to derive the Papapetrou equations of motion for spinning particles in curved space (including torsion). Based on talk given at: 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa-Zihuatanejo, Mexico, June 27-July 4, 1999.

gr-qc↗

arXiv1997

Physical Applications of a Generalized Clifford Calculus (Papapetrou equations and Metamorphic Curvature)

A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The generalized Dirac operator must now include differentiation with respect to these higher order geometric coordinates. In a Riemann space, where the magnitude and rank of geometric objects are preserved under displacement, these new terms modify the geodesics. One possible physical interpretation is natural coupling of the classical spin to linear motion, providing a new derivation of the Papapetrou equations. A generalized curvature is proposed for the Clifford manifold in which the connection does not preserve the rank of a multivector under parallel transport, e.g. a vector may be ``rotated'' into a scalar.

gr-qc↗

arXiv1993

Classification of Multivector Theories and the Modification of the Postulates of Physics

We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences. Specifically, spin-gauge formulations of gravitation and GUT which assume standard column spinors will require unnecessarily large matrix algebras. An extreme generalization is introduced, where wavefunctions are multivectors, in which multiple generations of particles naturally appear without resorting to increasing the size of the algebra. Further, this allows for two-sided (bilateral) operators, which can accomodate in excess of 10 times more gauge fields without increasing the algebraic representation. As this generalization encompasses all the essential features of the other categories, it is proposed to be the best path to new physics. [Summary of talk at 3rd International Conf on Clifford Algebras and Their Appl. in Physics, Deinze, Belgium May 1993].

gr-qc↗

arXiv1992

Clifford Algebra Derivation of the Characteristic Hypersurfaces of Maxwell's Equations

An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using 3D Clifford algebra (isomorphic to Pauli algebra spinorial formulation of electromagnetism). Subsequently one can more easily solve for the time evolution of both the electric and magnetic field simultaneously in terms of the fields evaluated only on a 3D hypersurface. The form of the special "characteristic" surfaces for which the time derivative of the fields can be singular are quickly deduced with little effort.

hep-th↗