Related papers: SU(N) Coherent States and Irreducible Schwinger Bo…
Super coherent states are useful in the explicit construction of representations of superalgebras and quantum superalgebras. In this contribution, we describe how they are used to construct (quantum) boson-fermion realizations and…
Eigenstates of general complex linear combination of SU(1,1) generators (su^c(1,1) algebraic coherent states (ACS)) are constructed and discussed. In case of quadratic boson representation ACS can exhibit strong both linear and quadratic…
We give a survey of several models of irreducible complementary series representations and their limits, special representations, for the groups SU(n,1) and SO(n,1), including new ones. These groups, whose geometrical meaning is well known,…
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form…
We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete…
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear…
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier…
The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the…
We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to…
The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N…
We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group and then by Lieb and…
A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra…
The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is…
The irreducible representations of SU(N) over a mixed quark-antiquark Fock space component have been studied for many years. In analogy to the case for the quark-only Fock space component, there exist efficient tools to classify the…
The supercoherent states of the RNS string are constructed using the covariant quantization and analogously the light cone quantization formalisms. Keeping intact the original definition of coherent states of harmonic oscillators, we extend…
Diagonalization of uncertainty matrix and minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear…
Following a general form for the Schwinger boson representation of the su(M+1) Lipkin model presented in the previous paper, three types of the orthogonal sets characterizing the su(3)-algebra are proposed. In these three, third is…
We present a systematic analysis on coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator.…
All finite dimensional irreducible representations of the simple Lie-Kac super algebra SU(2/1) are explicitly constructed in the Chevalley basis as complex matrices. For typical representations, the distinguished Dynkin label is not…
We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the…