Related papers: Polydimensional Relativity, a Classical Generaliza…
This paper presents a thoughful review of: (a) the Clifford algebra Cl(H_{V}) of multivecfors which is naturally associated with a hyperbolic space H_{V}; (b) the study of the properties of the duality product of multivectors and…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by…
The most familiar formalism for the description of geometry applicable to physics comprises operations among 4-component vectors and complex real numbers; few people realize that this formalism has indeed 32 degrees of freedom and can thus…
In three space dimensions, when a physical system possesses spherical symmetry, the dynamical equations automatically lead to the Legendre and the associated Legendre equations, with the respective orthogonal polynomials as their standard…
We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master…
Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are…
Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the…
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
The treatment of the principle of general covariance based on coordinate systems, i.e., on classical tensor analysis suffers from an ambiguity. A more preferable formulation of the principle is based on modern differential geometry: the…
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…
In this paper we give a thoughtful exposition of the hyperbolic Clifford algebra of multivecfors which is naturally associated with a hyperbolic space, whose elements are called vecfors. Geometrical interpretation of vecfors and…
Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the…