Related papers: Poincare Invariant Algebra From Instant to Light-F…
In this paper we achieve the quantization of a particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using group-theoretical methods. For this purpose, a fundamental role is played by contact,…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
Operator quantization of the WZNW theory invariant with respect to an affine Kac-Moody algebra $\hat g$ with constrained $\hat {u}(1)^d$ currents is performed using Dirac's procedure. Upon quantization the initial energy-momentum tensor is…
We introduce the magnetic angular momentum as a consequence of the structure of the sO(3) Lie algebra defined by the Feynman brackets. The Poincare momentum and Dirac magnetic monopole appears as a direct result of this framework.
Totally symmetric arbitrary spin fields in AdS space, conformal fields, conformal currents, and shadow fields in flat space are studied. Light-cone formulation for such fields, currents, and shadows is obtained. Use of the Poincare…
Explicit formulae for the projectors onto invariant subspaces of the $\operatorname{ad}^{\otimes 2}$ representation of the Lie algebras $so(N)$ and $sp(2r)$ have been found by means of the split Casimir operator. These projectors have also…
Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…
Many physical models are described by partial differential equations and the most important mathematical structure of the equations is governed by the corresponding linear partial differential operators. Those linear partial differential…
In recent years, algebras and modules of differential operators have been extensively studied. Equivariant quantization and dequantization establish a tight link between invariant operators connecting modules of differential operators on…
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…
A fully Poincare' covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare' group, and thus complies with the original Wigner approach to quantum symmetries. This…
The algorithm for inverting covariant exterior derivative is provided. It works for a sufficiently small star-shaped region of a fibered set - a local subset of a vector bundle and associated vector bundle. The algorithm contains some…
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…
We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a…
Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincare group only the Hamiltonian and the boost operators carry interactions, we offer an…
We define the angular momentum at null infinity in higher dimensions. The asymptotic symmetry at null infinity becomes the Poincare group in higher dimensions. This fact implies that the angular momentum can be defined without any…
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained…
Angular momentum at null infinity has a supertranslation ambiguity from the lack of a preferred Poincar\'e group and a similar ambiguity when the center-of-mass position changes as linear momentum is radiated. Recently, we noted there is an…
In this letter we derive a deformed Dirac equation invariant under the k-Poincare` quantum algebra. A peculiar feature is that the square of the k-Dirac operator is related to the second Casimir (the k-deformed squared Pauli-Lubanski…