Related papers: Ultracoherence and Canonical Transformations
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is shown for various…
We construct explicitly the quantum symplectic affine algebra $U_q(\widehat{sp}_{2n})$ using bosonic fields. The Fock space decomposes into irreducible modules of level -1/2, quantizing the Feingold-Frenkel construction for q=1.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit…
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…
The unitary irreducible representations of the covering group of the Poincare group P define the framework for much of particle physics on the physical Minkowski space P/L, where L is the Lorentz group. While extraordinarily successful, it…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the…
General semifinite factor representations of the diffeomorphism group of euclidean space are constructed by means of a canonical correspondence with the finite factor representations of the inductive limit unitary group. This construction…
We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and…
We show that for the strictly isospectral Hamiltonians, the corresponding coherent states are related by a unitary transformation. As an illustration, we discuss, the example of strictly isospectral one-dimensional harmonic oscillator…
A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg…
Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which $\hbar >0$ throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action…
Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…
Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations…
The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen…
Analogs of ordinary Gaussian coherent states on bosonic Fock spaces are constructed for the case of free Fock spaces, which appear to be natural mathematical structures suitable for description of large N matrix models.
The Bogoliubov transformation for a monopole boson induces an unitary transformation connecting the Fock spaces of initial and correlated boson-s. Here we provide a very simple method for deriving the analytical expression for the overlap…