Related papers: Pauli Terms Must Be Absent In Dirac Equation
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…
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…
Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the…
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on…
We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \bar{\psi}\sigma_{\mu\nu}\psi. In order to have only even terms in the chiral expansion, we consider…
A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, which are interpreted as single-particle fermion wave functions in four-dimensional spacetime. Use of a ``cylinder…
The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a…
The Standard Model of particle physics is derived from first principles from the free Dirac Lagrangian in 8-dimensional spacetime. Motivated by second quantization arguments, we embed the 4-dimensional Clifford algebra of the Dirac…
In this paper, we give the H\"ormander's $L^2$ theorem for Dirac operator over an open subset $\Omega\in\R^{n+1}$ with Clifford algebra. Some sufficient condition on the existence of the weak solutions for Dirac operator has been found in…
In this paper, we give the H\"ormander's $L^2$ theorem for Dirac operator over an open subset $\Omega\in\R^{n+1}$ with Clifford algebra. Some sufficient condition on the existence of the weak solutions for Dirac operator has been found in…
We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space $U_q(\g) \otimes \mathrm{cl}_q(\g)$ where the second tensor factor is a…
We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of spacetime. This point of view, as we…
In this paper we establish the three balls theorem for functions $u$ satisfying $Du=\lambda u$ in Clifford analysis, where $D$ is the Dirac operator. As an application, we generalize Hadamard's three circles theorem to monogenic function in…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
It is shown that classical Clifford algebras are group algebras of cyclic subgroups of arrowy rermutations. It is established that Euclidean 3-space, Pauli and Dirac algebras and groups of global guage transformations are corollary from the…
In standard quantum electrodynamics (QED), the so-called non-minimal (Pauli) coupling is suppressed for elementary particles and has no physical implications. Here, we show that the Pauli term naturally appears in a known family of Dirac…
Extended gamma matrix Clifford--Dirac and SO(1,9) algebras in the terms of $8 \times 8$ matrices have been considered. The 256-dimensional gamma matrix representation of Clifford algebra for 8-component Dirac equation is suggested. Two…
A unifying overview of the ways to parameterize the linear group GL(4.C) and its subgroups is given. As parameters for this group there are taken 16 coefficients G = G(A,B,A_{k}, B_{k}, F_{kl}) in resolving matrix G in terms of 16 basic…
The Dirac equation is a cornerstone of modern particle physics, which integrates special relativity and quantum mechanics into a consistent framework, yielding the prediction of electron and its antiparticle counterpart, positron. The Dirac…
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…