Related papers: Geometric algebra and particle dynamics
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…
The simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only, and reduces the…
Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect…
In this approach to discrete quantum gravity the basic structural element is a covariant causal set ($c$-causet). The geometry of a $c$-causet is described by a shell-sequence that determines the discrete gravity of a universe. In this…
The new scale-covariant formulation of the Dirac's Large Number Hypothesis (LNH) is proposed. The basic equations of LNH are formulated in the scale-covariant and "G-invariant" (invariant on the transformation law for G) form. On the basis…
Conventional relativistic electrodynamics is set on flat Minkowski spacetime, where all computable quantities are calculated from the flat metric $\eta_{\mu\nu}$. We can redefine the metric of spacetime from the Dirac algebra. In this…
We present a scheme of biquaternionic algebrodymamics based on a nonlinear generalization of the Cauchy-Riemann holomorphy conditions considered therein as fundamental field equations. The automorphism group SO(3,C) of the biquaternion…
Within the framework of geodetic brane gravity, the Universe is described as a 4-dimensional extended object evolving geodetically in a higher dimensional flat background. In this paper, by introducing a new pair of canonical fields…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…
This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…
A geometric approach to the standard model in terms of the Clifford algebra $% C\ell_{7}$ is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a simple geometric model involving extra…
Schr\"{o}dinger (Nature, v.169, 538 (1952)) noted that the complex matter field in the Klein-Gordon equation can be made real by a gauge transform, although charged fields are believed to require complex functions. Surprisingly, the result…
It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
Based on a fundamental symmetry between space, time, mass and charge, a series of group structures of physical interest is generated, ranging from C2 to E8. The most significant result of this analysis is a version of the Dirac equation…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…