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Publication:3743524
zbMath0605.22013MaRDI QIDQ3743524
Publication date: 1986
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coherent statesMaslov indexoscillator representationLorentz groupmetaplectic groupapplications to physicsreal Heisenberg nilpotent Lie groupnoncommutative harmonic analysis
Applications of Lie groups to the sciences; explicit representations (22E70) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Coherent states (81R30) Structure and representation of the Lorentz group (22E43) Research exposition (monographs, survey articles) pertaining to topological groups (22-02)
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Basic group theoretical and topological analysis, Even and odd charge coherent states and their non-classical properties, Renormalization group on the phase and the gamma functions for the generic Hamiltonian systems, Nonclassical depth of the phase state, Phase estimation, photon cloning and the Bernoulli map, Color-flavor transformation for the special unitary group, Exactly solvable models with time-dependent potentials, Bounds on the Segal-Bargmann transform of \(L^p\) functions, Positive-energy Dirac equation and generalized coherent states, The quantum mechanics of affine variables, \((1+1)\)-dimensional baryons from the SU\((N)\) color-flavor transformation, Quantization of scalar fields in curved background and quantum algebras, Quantization, group contraction and zero point energy, Non-commutative algebra of functions of 4-dimensional quantum Hall droplet, Chaos in a Hamiltonian description of interacting quantum spins, Complete signal processing bases and the Jacobi group, Quantum processes on phase space., Coherent states attached to Landau levels on the Riemann sphere, Solving the Schrödinger equation by reduction to a first-order differential operator through a coherent states transform, Symbolic Lie algebras manipulations using COMMON LISP, More on quantum groups from the quantization point of view, Rearrangement of energy bands: topological aspects, Polarization tomography of quantum radiation: theoretical aspects and operator approach, Consistency and axiomatization of a natural extensional combinatory logic, Poisson boundary of the dual of \(\text{SU}_q(n)\)., Lie-algebraic approach for pricing moving barrier options with time-dependent parameters, Quantization is geometry, after all, Weyl quantization and star products, Structure, dynamics and spectroscopy of single molecules: A challenge to quantum mechanics, The Moyal representation for spin, Quantum variance and ergodicity for the baker's map, Coherent states in geometric quantization, Quantum and classical fidelity for singular perturbations of the inverted and harmonic oscillator, Coherent state representations. 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Spin chains and integrable theories, Generalised harmonic oscillator systems and their Fock space description, Order-unit quantum Gromov--Hausdorff distance, A group-theoretic approach to the disentanglement of generalized squeezing operators, Pullback coherent states, squeezed states and quantization, Signatures of quantum chaos in the dynamics of bipartite fluctuations, The Bell experiment and the limitations of actors, Lie-algebraic approach for pricing zero-coupon bonds in single-factor interest rate models, Bi-coherent states as generalized eigenstates of the position and the momentum operators, Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states, Action-angle variables, ladder operators and coherent states, Fractals, coherent states and self-similarity induced noncommutative geometry, Hydrodynamic interpretation of generic squeezed coherent states: a kinetic theory, Quasienergy operators and generalized squeezed states for systems of trapped ions, Open strings in Lie groups and associative products, Coherent states of quantum linear rotator, Nonclassicality and decoherence of photon-added squeezed coherent Schrödinger kitten states in a Kerr medium, One-and-a-half quantum de Finetti theorems, Completeness of coherent state subsystems for nilpotent Lie groups, Introduction to coherent quantization, Degenerate \(r\)-Whitney numbers and degenerate \(r\)-Dowling polynomials via boson operators, From a quantum theory to a classical one, Generalized coherent states for \(q\)-deformed hyperbolic Pöshel-Teller potential, An approach to construct wave packets with complete classical-quantum correspondence in non-relativistic quantum mechanics, Coadjoint orbits and Kähler structure: examples from coherent states, Density operator in terms of coherent states representation with the applications in the quantum information, Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric 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levels, Emergent geometry of membranes, Reproducing Kernels in Coherent States, Wavelets, and Quantization, Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups, Some properties of Grassmannian $U(4)/U{(2)}^{2}$ coherent states and an entropic conjecture, Coherent states for Hopf algebras., Remark on a group-theoretical formalism for quantum mechanics and the quantum-to-Classical transition, Cavity-QED tests of representations of canonical commutation relations employed in field quantization, Algebraic approach to the Hulthen potential, On the oscillator realization of conformal U(2, 2) quantum particles and their particle-hole coherent states, Construction of the noncommutative complex ball, Spectral Theory and Representations\\ of Nilpotent Groups, Classical Yang-Mills observables from amplitudes, Controllability of quantum systems with \(SU(1,1)\) dynamical symmetry, Invariant metric on the extended Siegel-Jacobi upper half space, Gaussian distributions, Jacobi group, and Siegel-Jacobi space, The density theorem for discrete series representations restricted to lattices, Coherent state quantization of quaternions, Bargmann representation of quantum absorption refrigerators, Tuning co- and contra-variant transforms: the Heisenberg group illustration, Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators, États cohérents, théorie spectrale et représentations de groupes nilpotents, Bipartite entanglement of generalized Barut-Girardello nonlinear coherent states, Cross-Toeplitz operators on the Fock-Segal-Bargmann spaces and two-sided convolutions on the Heisenberg group, Solitons and giants in matrix model, P-representations in quantum optics, The fuzzy BTZ, Wavelet transform and orthogonal decomposition of space 𝐿² on the Cartan domain 𝐵𝐷𝐼(𝑞=2), Lie algebras and generalized thermal coherent states, Some identities on degenerate \(r\)-Stirling numbers via Boson operators, Quantification et analyse pseudo-différentielle, Pseudo-fermionic coherent states with time-dependent metric, An ``Anti-gleason phenomenon and simultaneous measurements in classical mechanics, Truncated conformal space approach for 2D Landau–Ginzburg theories, Delocalization properties at isolated avoided crossings in Lipkin–Meshkov–Glick type Hamiltonian models, Posterior distribution for negative binomial parameter \(p\) using a group invariant prior, Two-mode bosonic squeezing and symmetry breaking, Square integrable highest weight representations, Convergence of the Wick star product, Spin coherent states as energy eigenstates of two coupled oscillators, Semi-classical formula beyond the Ehrenfest time in quantum chaos. I: Trace formula, Homodyne detection and positive operator-valued measures, Asymptotic limits of SU(2) and SU(3) Wigner functions, Quantum complex Minkowski space, Magnetic backgrounds from generalised complex manifolds, Quadratic harnesses, $q$-commutations, and orthogonal martingale polynomials, Quantum mechanics of Klein-Gordon fields. II: Relativistic coherent states, Unnamed Item, Unnamed Item, Unnamed Item, The number radial coherent states for the generalized MICZ-Kepler problem, Unnamed Item, Wilson RG of noncommutative Φ44, Coherent-state overcompleteness, path integrals, and weak values, Entanglement in Phase Space, The generalized pair coherent states and the corresponding entangled coherent states, Integrability and non-integrability in quantum mechanics, Even and odd Wigner negative binomial states: Nonclassical properties, Moment map and gauge geometric aspects of the Schrödinger and Pauli equations, Entanglement of positive definite functions on compact groups, The Pauli principle revisited, Bose–Hubbard Hamiltonian: Quantum chaos approach, Coherent states of Landau–Aharonov–Casher levels, Unnamed Item, ProbabilisticQ-function distributions in fermionic phase-space, Coherent states on horospheric three-dimensional Lobachevsky space, sl(2)-modules by sl(2)-coherent states, Twisted Fock representations of noncommutative Kähler manifolds, Unnamed Item, Quantum entanglement and fixed-point bifurcations, Unnamed Item, Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters, Construction of the Noncommutative Rank I Bergman Domain, Radial coherent states for central potentials: The isotropic harmonic oscillator, Chiral metal as a ferromagnetic super spin chain, Generalized coherent states for \(q\)-oscillator associated with discrete \(q\)-Hermite polynomials, Asymptotic analysis of the EPRL model with timelike tetrahedra, Exact solutions of the Fokker-Planck equations with moving boundaries, REALIZATION OF DYNAMICAL GROUP FOR A SYMMETRIC WELL POTENTIAL tan2(πx/a) AND ITS CONTROLLABILITY, Ordered moments and relation to Radon transform of Wigner quasiprobability, Generalized husimi functions: Analyticity and information content, Robust quantum state engineering using coherent states on a truncated von Neumann lattice, Radon transform and pattern functions in quantum tomography, Boson Inverse Operators and a New Family of Two-photon Annihilation Operators, Thermal Coherent States and Thermal Squeezed States, Quantum Dynamics of a Nonlinear Birefringent Model with Anticorrelated Field States, Squeezed fermion states, Modular symmetry in parametrically excited quantum oscillators, Smooth Paths on Three-Dimensional Lattice, Semiclassical Description of Nonadiabatic Quantum Dynamics, Generalized Bosons and Coherent States, Complete Characterization of Arbitrary Quantum Measurement Processes, Quantum Time Evolution in Terms of Nonredundant Probabilities, Evolution of orbits and quantum correlation functions by quadratic Hamiltonians, A simple optical demonstration of geometric phases from multilayer stacks: The Wigner angle as an anholonomy, Coherent Schwartz distributions of the Heisenberg algebra and inverted oscillator, Exact time-evolution of a generalized two-dimensional quantum parametric oscillator in the presence of time-variable magnetic and electric fields, Fuzzy Schwarzschild (2 + 1)-spacetime, Truncated generalized coherent states, Exact solution and coherent states of an asymmetric oscillator with position-dependent mass, A gravitationally induced decoherence model using Ashtekar variables, Evolution of superoscillations for spinning particles, Harmonic analysis of covariant functions of characters of normal subgroups, Banach convolution modules of group algebras on covariant functions of characters of normal subgroups, Commutators on Fock spaces, On the extension of a family of projections to a positive operator-valued measure, Matrix-valued nonstationary frames associated with the Weyl–Heisenberg group and the extended affine group, Normal ordering associated with \(\lambda\)-Whitney numbers of the first kind in \(\lambda\)-shift algebra, Uncertainty relation for non-Hermitian operators, Phase spaces, parity operators, and the Born-Jordan distribution, Entangled coherent states and violations of Bell-CHSH inequalities, Coherent states associated with tridiagonal Hamiltonians, Bouncing Universe in loop quantum gravity: full theory calculation, The Fröhlich polaron at strong coupling. I: the quantum correction to the classical energy, Superspace realizations of the Bannai-Ito algebra, Ultra-quantum coherent states in a single finite quantum system, Optical Schrödinger cats with generalized coherent states, Orientational Order Parameters for Arbitrary Quantum Systems, Thermalization in quenched open quantum cosmology, The \(L^p-L^q\) boundedness and compactness of Fock projections, Classical off-shell currents, Normal ordering associated with \(\lambda\)-Stirling numbers in \(\lambda\)-shift algebra, SO*(2N) coherent states for loop quantum gravity, Unitary maps on Hamiltonians of an electron moving in a plane and coherent state construction, Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms, Ornstein-Uhlenbeck operators and holomorphic representations for a class of bounded symmetric domains, GeneralizedSU(2) covariant Wigner functions and some of their applications, Gabor analysis as contraction of wavelets analysis, Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits, Parametric models and information geometry on \(W^\star\)-algebras, Transmutations from the covariant transform on the Heisenberg group and an extended umbral principle, An alternative foundation of quantum theory, Sharp inequalities for coherent states and their optimizers, Metamorphism as a covariant transform for the SSR group, Multipartite strongly symmetric states and applications to geometric entanglement and classicality, Krylov complexity in quantum field theory, Entanglement and geometry from subalgebras of the Virasoro algebra, Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold, The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems, Dissipation, coherence and entanglement, Ladder operators with no vacuum, their coherent states, and an application to graphene, Oxidation, reduction and semi-classical limit for quantum matrix geometries, Rλ3-inspired black holes, Geometry and dynamics of Gaussian wave packets and their Wigner transforms, Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials, Symmetry in a space of conceptual variables, The close connection between the definition and construction of raised and decreased coherent states with the inverse generators in the algebraic description of quantum confined systems, Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator, Thermal nonlinear coherent states on a flat space and on a sphere, On an extension problem for density matrices, Spectral properties of the Dirichlet operator $\sum _{i=1}^{d}(-\partial _i^2)^{s}$∑i=1d(−∂i2)s on domains in d-dimensional Euclidean space, Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions, Squeezed states and Hermite polynomials in a complex variable, New observable effects of the Lorentz group, Generalized coherent states for massive spinless fields in the de Sitter space, Invariant wave equations, propagators and generalized coherent states over de Sitter space., Gauge theory on a quantum phase space, The groupoid of bifractional transformations, Generalized Grassmann variables for quantum kit (k-level) systems and Barut–Girardello coherent states for su(r + 1) algebras, Path integral and transfer matrix approach for a 1D nonequilibrium system with disorder, Coherent states à la Klauder-Perelomov for the Pöschl-Teller potentials, Coherent states, vacuum structure and infinite component relativistic wave equations, On the deformed cat state: Generating scheme via amplitude dispersion and the analysis of nonclassical features, Currents and charges for mixed fields, Quantum diffusions and Appell systems, Optimal bases of Gaussians in a Hilbert space: Applications in mathematical signal analysis, Fractional helicity, Lorentz symmetry breaking, compactification and anyons, Poisson structure and Moyal quantisation of the Liouville theory, \(k\)-component charge coherent states and their non-classical properties, \(\operatorname{SL}(2, \mathbb{C})\) Chern-Simons theory, a non-planar graph operator, and 4D quantum gravity with a cosmological constant: semiclassical geometry, Unified algebraic method to non-Hermitian systems with Lie algebraic linear structure, Construction of photon-added spin coherent states and their statistical properties, Analytic representations with theta functions for systems on ℤ(d) and on 𝕊, Disentanglement approach to quantum spin ground states: field theory and stochastic simulation, $Sp(4; \mathbb{R})$ squeezing for Bloch four-hyperboloid via the non-compact Hopf map, When geometric phases turn topological, Quantum and semi-classical aspects of confined systems with variable mass, New quantumness domains through generalized squeezed states, Wigner functions and coherent states for the quantum mechanics on a circle, Unnamed Item, Quantum (matrix) geometry and quasi-coherent states, SU(1, 1) covariant s-parametrized maps, Coherent states of the one-dimensional Dunkl oscillator for real and complex variables and the Segal–Bargmann transformation of Dunkl-type
