相关论文: Contemplations on Dirac's equation in quaternionic…

The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…

The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…

Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of…

In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…

Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…

In this note a simple extension of the complex algebra to higher dimension is proposed. Using the postulated algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra…

The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of…

It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac…

Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…

The two-dimensional Dirac equation has been widely used in graphene physics, the surface of topological insulators, and especially quantum scarring. Although a numerical approach to tackling an arbitrary confining problem was proposed…

We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac…

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are…

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…

It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the…

Here we follow the basic analysis that is common for real and complex variables and find how it can be applied to a quaternionic variable. Non-commutativity of the quaternion algebra poses obstacles for the usual manipulations; but we show…

As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…

We develop a systematic method to derive the Majorana representation of the Dirac equation in (1+3)-dimensions. We compare with similar approach in (2+2)-dimensions . We argue that our formalism can be useful to have a better understanding…

We extend the biquaternionic Dirac equation to include interactions with a background bosonic field. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter field and an electromagnetic field.…