Related papers: Noncommutative Coordinates Invariant under Rotatio…
The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic…
This paper introduces a systematic algorithm for deriving a new unitary representation of the Lorentz algebra ($so(1,3)$) and an irreducible unitary representation of the extended (anti) de-Sitter algebra ($so(2,4)$) on…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
In special relativity, spacetime algebra (STA) provides a powerful and insightful approach to an invariant formulation of physics. However, in this geometric algebra of spacetime, relativistic physics is usually considered a misnomer: STA…
Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all…
We consider three possible approaches to formulating coordinate transformations on position space associated with non-linear Lorentz transformations on momentum space. The first approach uses the definition of velocity and gives the…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
This paper describes a particularly didactic and transparent derivation of basic properties of the Lorentz group. The generators for rotations and boosts along an arbitrary direction, as well as their commutation relations, are written as…
Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…
Within the framework of warped convolutions we deform the massless free scalar field. The deformation is performed by using the generators of the special conformal transformations. The investigation shows that the deformed field turns out…
We study the quantum mechanics of a system with inverse square potential in noncommutative space. Both the coordinates and momentums are considered to be noncommutative, which breaks the original so(2,1) symmetry. The energy levels and…
It is shown that the noncommutative Lorentz metric satisfies so-called nonpropagating waves. The long-range forces are obtained as a description of these wave motions. It leads to the natural introduction of the field values (group velocity…
Unidirectional transport and localized cyclotron motion are two opposite physical phenomena. Here, we study the interplay effects between them on nonreciprocal lattices subject to a magnetic field. We show that, in the long-wavelength…
We show how an induced invariance of the massless particle action can be used to construct an extension of the Heisenberg canonical commutation relations in a non-commutative space-time.
The aim of this paper is to find out how would possible space non-commutativity (NC) alter the QM solution of the Coulomb problem. The NC parameter lambda is to be regarded as a measure of the non-commutativity - setting lambda = 0 means a…
We describe and solve three puzzles arising in covariant and supertranslation-invariant formulas for the flux of angular momentum and other Lorentz charges in asymptotically flat spacetimes: 1) Supertranslation-invariance and covariance…
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we…
The non-relativistic hydrogen atom and the Zwanziger problem have the same dynamical symmetry for bound and scattering states.We show that this is also true for a Hilbert space which is non-commutative in co-ordinates. The group structure…