Related papers: Relativistic Operator Description of Photon Polari…
It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ''modular localization'' is not only…
We review the method for constructing local relativistic fields corresponding to the Bargmann-Wigner wave functions that describe the unitary irreducible representations of the $4D$ Poincar\'{e} group. The method is based on the use of the…
This is mainly a lecture note taken by myself following Weinberg's book, but also contains some corrections to the abuse of mathematical treatment. This article discusses projective unitary representations of Poincare group on the single…
We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations of the Poincar\'e group, labelled by…
The polarization operator in a constant and homogeneous magnetic field of arbitrary strength is investigated on mass shell. The calculations are carried out at all photon energies higher the pair creation threshold as well as lower this…
The behavior of an electron spin interacting with a linearly polarized laser field is analyzed. In contrast to previous considerations of the problem, the initial state of the electron represents a localized wave packet, and a spatial…
We define a Hermitian phase operator for zero mass spin one particles (photons) by taking account polarization. The Hilbert space includes the positive helicity states and negative helicity states with opposite circular polarization. We…
We show that a modification of Wigner's induced representation for the description of a relativistic particle with spin can be used to construct spinors and tensors of arbitrary rank, with invariant decomposition over angular momentum. In…
The Biedenharn type relativistic wavefunctions are considered on the group manifold of the Poincar\'{e} group. It is shown that the wavefunctions can be factorized on the group manifold into translation group and Lorentz group parts. A…
We give a direct link between description of Dirac particles in the abstract framework of unitary representation of the Poincar\'e group and description with the help of the Dirac equation. In this context we discuss in detail the spin…
We construct one-particle states as unitary, irreducible representations of Poincare group in front form, characterized by a special null vector, dubbed reference vector. We demonstrate that this construction has massive-massless…
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…
A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in…
Polarisation is described by an $SU(2)$ wavefunction due to macroscopic coherence of photons emitted from a ubiquitous laser source, and thus, a laser pulse is expected to behave as a macroscopic quantum bit (qubit), i.e., a qubit realised…
The capabilities of some approaches to the relativistic description of hadronic states with any rest spin are analysed. The key feature in the Wigner's construction of irreducible representations of the Poincare group which makes this…
In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the…
For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for…
We consider emission of a photon by an electron in the field of a strong laser wave. Polarization effects in this process are important for a number of physical problems. We discuss a probability of this process for circularly polarized…
The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle…
Although there are many proposals of relativistic spin observables, there is no agreement about the adequate definition of this quantity. This problem arises from the fact that, in the present literature, there is no consensus concerning…