Related papers: Cubic root of Klein-Gordon equation
We review a recently proposed Clifford-algebra approach to elementary particles. We start with: (1) a philosophical background that motivates a maximally symmetric treatment of position and momentum variables, and: (2) an analysis of the…
We employ the Dirac procedure to quantize the self-dual massive Kalb-Ramond-Klein-Gordon model in $2+1$ dimensional spacetimes. The canonical fields are expressed in terms of $2$-surfaces and signed points, ensuring the automatic…
Let A be a cosemisimple Hopf *-algebra with antipode S and let $\Gamma$ be a left-covariant first order differential *-calculus over A such that $\Gamma$ is self-dual and invariant under the Hopf algebra automorphism S^2. A quantum Clifford…
It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra…
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…
Several complications arise in quantum field theory because of the infinite many degrees of freedom. However, the distinction between one-particle and many-particle effects -- mainly induced by the vacuum -- is not clear up to now. A field…
A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field,…
Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincar\'e gauge theory (PGT). Thus, the gravitational field variables are the orthonormal coframe (tetrad) and…
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 solve Klein-Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The presented solution is the simplest ever obtained for quaternionic quantum theories, and the…
We propose a formal framework for a noncommutative Kadomtsev--Petviashvili (KP) hierarchy which is covariant under the action of $SU(3)$ and compatible with a Lorentzian structure encoded in a twisted quaternionic (or Clifford) algebra. The…
We show that complex representations of Clifford algebra can always be reduced either to a real or to a quaternionic algebra depending on signature of complex space thus showing that complex spinors are unavoidably either real Majorana…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
Deformed $\mathfrak{g}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and…
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e invariance. We determine the constraints…
A special class of higher curvature theories of gravity, Ricci Cubic Gravity (RCG), in general d dimensional space-time has been investigated in this paper. We have used two different approaches, the linearized equations of motion and…
Exact solutions of Dirac equation in two spatial dimensions in the Coulomb field are obtained. Equation which determines the so-called critical charge of the Coulomb field is derived and solved for a simple model.
Finite-dimensional representations of the proper orthochronous Lorentz group are studied in terms of spinor representations of the Clifford algebras. The Clifford algebras are understood as an `algebraic covering' of a full system of the…
A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…
Given the real Clifford algebra of a quadratic space with a given signature, we define a new product in this structure such that it simulates the Clifford product of a quadratic space with another signature different from the original one.…