Related papers: Lorentz Group in Condensed Matter Physics
Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of…
In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in $R^{1,d-1}$ is investigated. The introduction of a new generator is…
Based on the principle of relativity with two universal constants (c, l) and in the inertial motion group IM(1,3)\sim PGL(5,R), with Lorentz isotropy, in addition to Poincar\'e group of Einstein's SR the dual Poincar\'e group preserves the…
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…
The symmetry of vacuum is characterized by the Lorentz group with the parameter $c$. Physical space inside the homogeneous optical medium should be described by the Lorentz group with the parameter $c/n$, where $n$ is the refractive index…
We present a unified group-theoretical framework for superparticle theories. This explains the origin of the ``twistor-like'' variables that have been used in trading the superparticle's $\kappa$-symmetry for worldline supersymmetry. We…
This paper describes a particularly didactic and transparent derivation of basic properties of the Lorentz group. The generators for rotations and boosts along an arbitrary direction, as well as their commutation relations, are written as…
Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of General Relativity. One of these is Lorentz symmetry which states that physical phenomena appear the same for all inertially moving observers. We…
Quantization of relativistic point particles coupled to three-dimensional Einstein gravity naturally leads to field theories living on the Lorentz group in their momentum representation. The Lie group structure of momentum space can be…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
Bose-Einstein condensation of light in 2D is characterized by two classical fields corresponding to two polarizations of light as well as by the distribution of dye molecules inducing light thermalization through dipolar transition. In the…
We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel…
The dipole cutoff behavior for the proton form factor has been and still is one of the major issues in high-energy physics. It is shown that this dipole behavior comes from the coherence between the Lorentz contraction of the proton size…
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…
We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2…
The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…
Contrary to the usual belief, by carefully examining the operation of parity transformation on the $(1,0)\oplus(0,1)$ mesons in the generalized canonical representation, we establish that the $(j,0)\oplus(0,j)$ meson-antimeson pair have…
Matrix elements of irreducible representations of the Lorentz group are calculated on the basis of complex angular momentum. It is shown that Laplace-Beltrami operators, defined in this basis, give rise to Fuchsian differential equations.…
The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions…
The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists…