Related papers: Wigner rotation and Euler angle parametrization
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We examine deformed Poincar\'e algebras containing the exact Lorentz algebra. We impose constraints which are necessary for defining field theories on these algebras and we present simple field theoretical examples. Of particular interest…
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties…
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…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
The second part of the article is devoted to field transfers by diffraction that are represented by fractional Fourier transformations whose orders are complex numbers. The corresponding effects on the Wigner distributions associated with…
We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore,…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
We revisit the classic Wigner semi-circle from two different angles. One consists in studying the Stieltjes transform directly on the real axis, which does not converge to a fixed value but follows a Cauchy distribution that depends on the…
We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…
An electron moving on plane in a uniform magnetic field orthogonal to plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schroedinger equation…
The Uehling contribution to the Lamb shift can be computed exactly in terms of the Uehling potential function. However derivations of this function are complex involving avoiding divergences using intricate techniques from early quantum…
The method of deforming free fields by using multiplication operators on Fock space, introduced by G. Lechner in [11], is generalized to a charged free field on two- and three-dimensional Minkowski space. In this case the deformation…
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…
A novel invariant decomposition of diagonalizable $n \times n$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $\mathfrak{su}(3)$ Lie algebra elements…
We consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
In the first part of the thesis, and after an introduction to certain models of modified gravity, we study consistent Lagrangians for Lorentz invariant (massive and massless) spin-2 and spin-3/2 particles in flat space. The second part of…