Related papers: Relativistic Wave Equations in the Helicity Basis
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…
The basic principles of generalization of the group theoretical approach to the relativistic wave equations on curved spaces are examined. The general method of the determination of wave equations from the known symmetry group of a…
Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac…
We derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter…
I here investigate what is arguably the most significant residual challenge for the proposal of phenomenologically viable "DSR deformations" of relativistic kinematics, which concerns the description of composite particles, such as atoms.…
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…
A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. They are the pseudoclassical basis of the positive energy $({1\over 2},0)$ [or…
Scalar, baryon and vector--current densities in coordinate and momentum space are calculated within a relativistic mean--field model. The role of the low components of the bound nucleon wave function is investigated in detail for different…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…
We construct coherent states of the massless and massive representations of the Poincar\'e group. They are parameterised by points on the classical state space of spinning particles. Their properties are explored, with special emphasis on…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
We construct an infinite component relativistic wave equation which is a linear first order differential equation identical in form to a Dirac like equation, describing composite fields possessing multiple spin and energy states. The main…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
Different bases for the spin-1 density matrix are discussed to clarify the connection between its components and observables measured in heavy-ion collisions. The theoretical advantage of using the adjoint representation for spin matrices…
Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and…
The relativistic Lagrangian for a spinning particle in an electromagnetic field is derived from the known Lagrangian in the particle's rest frame. The resulting relativistic Stern-Gerlach and Thomas precession forces on the particle are…
Massive and massless potentials play an essential role in the perturbative formulation of particle interactions. Many difficulties arise due to the indefinite metric in gauge theoretic approaches, or the increase with the spin of the UV…
We study singular hypersurfaces in tensor multi-scalar theories of gravity. We derive in a distributional and then in an intrinsic way, the general equations of junction valid for all types of hypersurfaces, in particular for lightlike…