Related papers: Dynamics with unitary phase operator:implications …
Phase operators and phase states are introduced for irreducible representations of the Lie algebra su(3) using a polar decomposition of ladder operators. In contradistinction with su(2), it is found that the su(3) polar decomposition does…
From SUSY ladder operators in momentum space of a neutron in the magnetic field of a linear current, we construct $2\times 2$ matrix operators that together with the z-component of the angular momentum satisfy the su(2) Lie algebra. We use…
The Lie algebra of the classical group SU(2) is constructed from two quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the ladder…
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed…
We demonstrate a model which captures certain attractive features of $SU(5)$ theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras $\mathbb{R}$,…
The Lie algebra su(2) of the classical group SU(2) is built from two commuting quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the…
We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the…
The paper \cite{BM} proposed a construction of a twisted representation of the lattice vertex algebra corresponding to the Milnor lattice of a simple singularity. The main difficulty in extending the above construction to an arbitrary…
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root…
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…
We define a unitary phase operator for photons in a single momentum mode. The operator acts on a Hilbert space with basis consisting of all number states in both polarizations. The Susskind Glogower operator, ${\hat{E}} = e^{i \hat{\phi}}$,…
It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra generated by metaplectic operators and by pseudodifferential…
In the weak-coupling regime of the continuous theories, two sets of one-loop renormalization group equations are derived and solved to disclose the phase diagrams of the antiferromagnetic generalized two-leg spin-1/2 ladder under the effect…
Principal axis transformation is performed for a Lagrangian with a U(1)-SU(2) mixing term, that can cause a SU(2) deconfining transition.
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…
The low-energy properties of the SU(4) spin-orbital model on a two-leg ladder are studied by a variety of analytical and numerical techniques. Like in the case of SU(2) models, there is a singlet-multiplet gap in the spectrum, but the…
We address the problem of phase shift operator acting as time evolution operator in Pegg-Barnett formalism. It is argued that standard shift operator is inconsistent with the behaviour of the state vector under cyclic evolution. We consider…
We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can…
Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra,…