相关论文: Extra Dirac Equations

We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…

We present a novel paradox in special relativity together with its solution. We call it the four particles paradox. The purpose of this paradox is pedagogical and therefore directed towards students and lecturers of physics. Even if most…

SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the…

The Lorentz group is the fundamental language for space-time symmetries of relativistic particles. This group can these days be derived from the symmetries observed in other branches of physics. It is shown that this group can be derived…

The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…

I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…

We describe relativistic particles with spin as points moving in phase space $X=T^* R^{1,3}\times C^2_L\times C^2_R$, where $T^* R^{1,3}=R^{1,3}\times R^{1,3}$ is the space of coordinates and momenta, and $C^2_L$ and $C^2_R$ are the spaces…

Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are…

The present theory is closely related to Dirac's equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac…

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin $(j > 1/2)$ using chiral representations of the Lorentz group, i.e. the $(j,0)$ and $(0,j)$ representations and their…

We give an interpretation of J-spaces in terms of symmetric spectra in symmetric sequences. As application we show how one can define graded endomorphism objects in a general situation. As example we discuss the motivic bigraded…

The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible states of the particle are just kinematical modifications of any one of them. In this way instead of describing…

We discuss recent results on orbifold compactifications with (0,2) world sheet supersymmetry and continuous Wilson lines, emphasizing the role of modular symmetries. (This work is a contribution to the proceedings of the joint US Polish…

I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie…

Using the language of the Geometric Algebra, we recast the massive Dirac bispinor as a set of Lorentz scalar, vector, bivector, pseudovector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism.…

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…

In these notes we give an introductory unified treatment to the topics of special relativity, Lorentz transformations and the Lorentz group, Einstein velocitiy addition, and gyrogroups and gyrovector spaces. An effort has been made to…

By Very Special Relativity (VSR) we mean descriptions of nature whose space-time symmetries are certain proper subgroups of the Poincar\'e group. These subgroups contain space-time translations together with at least a 2-parameter subgroup…

It is shown that the use of extended sets of irreducible representations of the Lorentz group opens new possibilities for the theory of relativistic wave equations from the point of view of the space-time description of both the internal…