9 papers
Dimensionally Democratic Calculus and Principles of Polydimensional Physics
William M. Pezzaglia
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 i…
Polydimensional Supersymmetric Principles
William M. Pezzaglia
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…
Physical Applications of a Generalized Clifford Calculus (Papapetrou equations and Metamorphic Curvature)
William M. Pezzaglia
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 ident…
Should Metric Signature Matter in Clifford Algebra Formulations of Physical Theories?
William M. Pezzaglia, John J. Adams
Standard formulation is unable to distinguish between the (+++-) and (---+) spacetime metric signatures. However, the Clifford algebras associated with each are inequivalent, R(4)…
Polydimensional Relativity, a Classical Generalization of the Automorphism Invariance Principle
William M. Pezzaglia
The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space…
Multivector Solutions to the Hyper-Holomorphic Massive Dirac Equation
William M. Pezzaglia
Attention is given to the interface of mathematics and physics, specifically noting that fundamental principles limit the usefulness of otherwise perfectly good mathematical genera…