Related papers: Relativistic probability amplitudes II. The photon
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…
We derive a simple expression for the photon helicity and polarisation-flip probabilities in arbitrary background fields, in the low energy regime. Taking the background to model a focused laser beam, we study the impact of pulse shape and…
We continue the program, presented in previous Symposia, of discretizing physical models. In particular we calculate the integral Lorentz transformations with the help of discrete reflection groups, and use them for the covariance of…
Recently, a bundle theoretic description of massive single-particle state spaces, which is better suited for Relativistic Quantum Information Theory than the ordinary Hilbert space description, has been suggested. However, the mathematical…
The Inonu-Wigner contraction is applied to special relativity and the little groups of the Lorentz group. If the O(3) symmetry group for massive particle is boosted to an infinite-momentum frame, it becomes contracted to a combination of…
We provide a detailed decomposition of Wigner's particles, defined as unitary irreducible representations of the Poincar\'e group, in terms of unitary representations of its Lorentz subgroup. As pointed out before us, this decomposition…
The time-energy uncertainty relation is discussed for a relativistic massless particle. The Lorentz-invariant uncertainty relation is obtained between the root-mean-square energy deviation and the scatter of registration time. The…
We show how Wigner's little group approach to the representation theory of Poincar\'e group may be generalized to the case of $\kappa$-deformed Poincar\'e group. We also derive the deformed Lorentz transformations of energy and momentum. We…
Assuming trivial action of Euclidean translations of the little group, we derive a simple correspondence between massless field representations transforming under the full generalized even dimensional Lorentz group, and highest weight…
Poincar\'e invariance is a well-tested symmetry of nature and sits at the core of our description of relativistic particles and gravity. At the same time, in most systems Poincar\'e invariance is not a symmetry of the ground state and is…
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…
A relative position 4-vector is constructed for two spin-zero particles. Some advantages of this relative position over Bakamjian-Thomas are pointed out. The centre-of-mass (CM) and relative positions and momenta are an explicit realisation…
Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum.…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…
Relativistic resonances and decaying states are described by representations of Poincar\'e transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$-matrix, the…
Heisenberg's uncertainty relation means that one observer cannot know an exact position and velocity for another (finite mass) observer. By contrast, the Poincare transformation of classical special relativity assumes that one observer…
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…
In a generalized Heisenberg/Schroedinger picture, the unitary representations of the Lorentz group may, for a massive relativistic particle, be used to attribute to waves an extra wavelength that is longer than the de Broglie wavelength.…
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 conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…