相关论文: The Lorentz group and the Kronecker product of mat…
In this note we present explicit and elementary formulas for the correspondence between the group of special Lorentz transformation $SO^+(3,1)$, on the one hand, and its spin group $SL(2,\mathbb{C})$, on the other hand. Although we will not…
A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over a simple non-division algebra. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…
A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over the hyperbolic number system. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…
For those finite-matrix representations of the Lorentz group of rotations/boosts with spin $(A,B)\oplus(C,D)$ that can also represent translations, two possible translation subgroups qualify. Of these two, one must be selected, and one…
We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
In this work we provide an elementary derivation of the indefinite spin groups in low-dimensions. Our approach relies on the isomorphism of Cl(p+1, q+1) to the algebra 2x2 matrices with entries in Cl(p,q), simple properties of Kronecker…
The quantum analogues of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indiceswe construct a quantum Minkowsky metric. In this framework, we show explicitely the correspondance…
Spinor structure is understood as a totality of tensor products of biquaternion algebras, and the each tensor product is associated with an irreducible representation of the Lorentz group. A so-defined algebraic structure allows one to…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam…
Some facts of the theory of the Lorentz group are specified for looking at the problems of light polarization optics in the frames of vector Stokes-Mueller and spinor Jones formalism. In view of great differences between properties of…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
It is shown that a subgroup of $SL(2,{\mathbb H})$, denoted $Spin(2,{\mathbb H})$ in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally isomorphic to the restricted Lorentz group,…
The goal of this paper is to develop a systematic method of locating the Mueller matrices within the class of the matrices of the real group SL(4, R). The main idea is to construct the general transformation of the group SL(4, R) (whose…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation E x' + A x = 0. Such an equation is invariant by changes of variables,…
Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum.…
We comment on the article by M. Ozdemir and M. Erdogdu. We indicate that the exponential map onto the Lorentz group can be obtained in two elementary ways. The first way utilizes a commutative algebra involving a conjugate of a…