Related papers: General Wigner Rotations in $D$ Dimensions
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
We discuss transormation laws of electric and magnetic fields under Lorentz transformations, deduced from the Classical Field Theory. It is found that we can connect the resulting expression for a bivector formed with those fields, with the…
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…
Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated, for example, in the following way: Every bijective transformation on the set L of all 1-dimensional subspaces of a…
We find relations between quantities defining geometry and quantities defining the length of a curve in geometries underlying Electromagnetism and unified model of Electromagnetism and Gravitation. We show that the length of a vector…
We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to the previous works. We…
We describe a five-dimensional analogue of Wigner's operator equation ${\mathbb W}_a = \lambda P_a$, where ${\mathbb W}_a $ is the Pauli-Lubanski vector, $P_a$ the energy-momentum operator, and $\lambda$ the helicity of a massless particle.…
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action…
We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the…
The internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The $O(3)$-like little group for a massive particle at rest and the $E(2)$-like little group of a massless particle are two different…
Whatever dark matter is, it must be one irreducible unitary representation of the extended Lorentz group or another. We here develop a formalism of mass dimension one fermions and bosons of spin one half, and show that they provide natural…
We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in…
We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp-waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for…
Using a position operator obtained for spin 1 particles by the present author and Wigner, we obtain a quantum relativistic result for the hidden momentum force experienced by particles with structure. In particular, our result applies to…
Wigner's little group of a massless particle is ISO(2) which contains rotation and two translations. As well-known, eigenvalues of the rotation are helicity. On the other hand, by S. Weinberg et al., it has been shown that two translations…
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…
The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massive spinless particle in four-dimensional space-time are studied. It is shown that the modified system remains spinless and possesses extended…
The parity violation at the level of weak interactions and other similar discrete symmetries breaking show that the invariance of laws under the full group of Lorentz transformations can not be taken granted. We examine the principle of…
For D=4 theories of a single U(1) gauge field strength coupled to gravity and matters, we show that the electric-magnetic duality can be formulated as an invariance of the actions. The symmetry is associated with duality rotation acting…
The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an…