Related papers: Lorentz Group in Ray and Polarization Optics
The Lorentz group Lor$_{1,3}=$SO$_0(1,3)$ has two point fixgroups, namely SO$(3)$ for time-like translations and SO$_0(1,1)\times R^2$ for light-like translations. However, for light-like translations it is reasonable to consider a line…
Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics,…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a…
In these lecture notes we review the isomorphism between the (connected) Lorentz group and the set of conformal transformations of the sphere. More precisely, after establishing the main properties of the Lorentz group, we show that it is…
In this paper we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the group SL (2, C) and the Lorentz group, we design a…
The Gupta-Bleuler formalism for photons is derived from induced representation theory. The representation for the little group for massless particles, the two dimensional Euclidian group, is chosen to be the four dimensional nonunitary…
We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor and we study the corresponding…
The starting point of the theory of Special Relativity$^1$ is the Lorentz transformation, which in essence describes the lack of absolute measurements of space and time. These effects came about when one applies the Second Relativity…
An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic…
In the present note the expansion of the wave function of a massless particle (with the definite value of its helicity) over the untary irreducible representaions of the Lorentz group (defined on the light cone) is used as for the analog of…
In this paper, we develop the quantum theory of particles that has discrete Poincar\'{e} symmetry on the one-dimensional Bravais lattice. We review the recently discovered discrete Lorentz symmetry, which is the unique Lorentz symmetry that…
Special Relativity (SR) kinematics is derived from very intuitive assumptions. Contrary to standard Einstein's derivation, no light signal is used in the construction nor it is assumed to exist. Instead we postulate the existence of two…
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.
Einstein's reply to Weyl about the importance in General Relativity of the identity of the sources of spectral lines is well know. We show that, already in Special Relavitity, Einstein's definition of the unit of time from the frequency of…
Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…
We generalize Zwanziger's pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter…
We present an in-depth investigation of the ${\rm SL}(2,\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and…