Related papers: Forces on an exterior algebra bundle
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with…
In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions made by several collegues. The treatment is…
We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical…
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained…
Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of…
We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional, while an "internal" space is enlarged.…
In this work, we interpret part of the boundary conditions as external sources in order to solve the integrability problem present in the computation of surface charges associated to gauge symmetries in the hamiltonian formalism. We start…
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
It is shown that Einstein's equations on the brane can be received from the multi-dimensional vector field equations in pseudo-Euclidean space. The idea is based on the observation that the brane geometry can be equivalently described by…
We consider four subsets of the complexified spacetime algebra, namely the real even part, the real odd part, the imaginary even part and the imaginary odd part. This naturally leads to the four connected components of the Lorentz group,…
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine…
In a recent publication the I showed how the geometric algebra ${G}_{4,1}$, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper…
By carefully analyzing the geodesic motion of a test particle in the bulk of brane worlds, we identify an extra force which is recognized in spacetime of one lower dimensions as a non-gravitational force acting on the particle. Such extra…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for…