Related papers: Explicit form for the most general Lorentz transfo…
The formation of a confining string (or a p-brane) in a Poincare' invariant theory breaks spontaneously this symmetry which is thereby realized non-linearly in the effective action of these extended objects. As a consequence the form of the…
Covariantly we reformulate the description of a spinning particle in terms of the Poincar\'{e} group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the…
The Lorentz Transformations are derived without any linearity assumptions and without assuming that y and z coordinates transform in a Galilean manner. Status of the invariance of the speed of light is reduced from a foundation of the…
The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
We obtain an explicit simple formula for the coefficients of the asymptotic expansion for the factorial of a natural number,in terms of derivatives of powers of an elementary function. The unique explicit expression for the coefficients…
The Courant-Snyder theory for two-dimensional coupled linear optics is presented, based on the systematic use of the real representation of the Dirac matrices. Since any real $4\times 4$-matrix can be expressed as a linear combination of…
For the rigid, nonrotating motion of an extended charge in an arbitrary electromagnetic field, an equation of motion is derived by Lorentz-invariantly calculating the 4-Lorentz force = external 4-force + 4-self-force, acting upon the…
The positivity of the Bondi mass has been proven in 4 dimensions, but in higher dimensions the issue remains open. The formalism of the present paper has been developed to investigate this and is well suited to the higher dimensional case.…
4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied…
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…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition…
The formula for the relativistic Doppler effect is investigated in the context of two compelling invariance axioms. The axioms are expressed in terms of an abstract operation generalizing the relativistic addition of velocities. We prove…
It is well known that a sequence of two non-collinear pure Lorentz transformations (boosts) is not a boost again, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. The formation of this rotation is visually illustrated…
We show that the requirement of Poincare invariance (more specifically invariance under boosts/rotations that mix brane directions with transverse directions) places severe constraints on the form of actions describing multiple D-branes,…
We calculate the critical exponents for Lorentz-violating O($N$) $\lambda\phi^{4}$ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An…
We give a brief overview of the BRST approach to the gauge invariant Lagrangian formulation for free massive higher-spin bosonic fields focusing on two specific aspects. First, the theory is considered in four dimensional flat space in…
In this paper we discuss the notion of reducibility for matrix weights and introduce a real vector space $\mathcal C_\mathbb{R}$ which encodes all information about the reducibility of $W$. In particular a weight $W$ reduces if and only if…