2001, Studies in advanced mathematics, ISBN 9781584880011, xi, 278

Book

IEEE Transactions on Signal Processing, ISSN 1053-587X, 10/2008, Volume 56, Issue 10, pp. 4905 - 4918

.... Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted...

Data compression | Quantization | sensor networks | Telecommunication computing | Application software | probabilistic quantization | Concurrent computing | Average consensus | Signal processing algorithms | Bandwidth | Signal processing | Computer networks | dithering | Distributed algorithms | Dithering | Probabilistic quantizationsensor networks | DEVIATION | distributed algorithms | BOUNDS | average consensus | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mobile communication systems | Wireless communication systems | Analysis | Geometric probabilities | Distributed processing (Computers) | Research | Probabilities | Quantum theory | Combinatorial probabilities | Studies | Algorithms | Intervals | Mathematical analysis | Evolution | Dynamical systems | Standards | Convergence

Data compression | Quantization | sensor networks | Telecommunication computing | Application software | probabilistic quantization | Concurrent computing | Average consensus | Signal processing algorithms | Bandwidth | Signal processing | Computer networks | dithering | Distributed algorithms | Dithering | Probabilistic quantizationsensor networks | DEVIATION | distributed algorithms | BOUNDS | average consensus | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mobile communication systems | Wireless communication systems | Analysis | Geometric probabilities | Distributed processing (Computers) | Research | Probabilities | Quantum theory | Combinatorial probabilities | Studies | Algorithms | Intervals | Mathematical analysis | Evolution | Dynamical systems | Standards | Convergence

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2018, Volume 331, pp. 941 - 951

We study a notion of pre-quantization for b-symplectic manifolds. We use it to construct a formal geometric quantization of b-symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight...

Formal geometric quantization | b-Symplectic manifolds | Poisson manifolds | MATHEMATICS | RIEMANN-ROCH FORMULAS | NONCOMPACT MANIFOLDS | MULTIPLICITIES FORMULA | Geometria diferencial | Geometria | Geometric quantization | Quantització geomètrica | Matemàtiques i estadística | Àrees temàtiques de la UPC

Formal geometric quantization | b-Symplectic manifolds | Poisson manifolds | MATHEMATICS | RIEMANN-ROCH FORMULAS | NONCOMPACT MANIFOLDS | MULTIPLICITIES FORMULA | Geometria diferencial | Geometria | Geometric quantization | Quantització geomètrica | Matemàtiques i estadística | Àrees temàtiques de la UPC

Journal Article

Annalen der Physik, ISSN 0003-3804, 2018, Volume 530, Issue 5, pp. 1700415 - n/a

A fundamental problem regarding the Dirac quantization of a free particle on an N...

geometric potential | geometric momentum | hypersurfaces | constrained Hamiltonian | quantization | CENTRIPETAL FORCE LAW | FREE PARTICLE | PHYSICS, MULTIDISCIPLINARY | SPACE | MOTION | CANONICAL QUANTIZATION | CONSTRAINTS | QUANTUM-MECHANICS | RIEMANNIAN MANIFOLD | EQUATION | CURVED SURFACE | Measurement | Curvature | Schroedinger equation

geometric potential | geometric momentum | hypersurfaces | constrained Hamiltonian | quantization | CENTRIPETAL FORCE LAW | FREE PARTICLE | PHYSICS, MULTIDISCIPLINARY | SPACE | MOTION | CANONICAL QUANTIZATION | CONSTRAINTS | QUANTUM-MECHANICS | RIEMANNIAN MANIFOLD | EQUATION | CURVED SURFACE | Measurement | Curvature | Schroedinger equation

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 10/2017, Volume 355, Issue 1, pp. 97 - 144

...). We show that the BV quantization (in Costello’s sense) of the model, which produces a perturbative quantum field theory, can be obtained via the configuration space method of regularization due to Kontsevich...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | INVARIANTS | TOPOLOGICAL FIELD-THEORY | Algebra

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | INVARIANTS | TOPOLOGICAL FIELD-THEORY | Algebra

Journal Article

Fortschritte der Physik, ISSN 0015-8208, 2019, Volume 67, Issue 8-9, p. 1910022

We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of nonassociativity in quantum mechanics with magnetic monopoles...

bundle gerbes | higher quantization | nonassociative geometry | non-geometric strings | magnetic monopoles | STRINGS | INTEGRATION | PHYSICS, MULTIDISCIPLINARY | DEFORMATION QUANTIZATION | MONOPOLES | Conferences, meetings and seminars | Conferences and conventions

bundle gerbes | higher quantization | nonassociative geometry | non-geometric strings | magnetic monopoles | STRINGS | INTEGRATION | PHYSICS, MULTIDISCIPLINARY | DEFORMATION QUANTIZATION | MONOPOLES | Conferences, meetings and seminars | Conferences and conventions

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2009, Volume 13, Issue 5, pp. 1445 - 1518

.... This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M, omega) is the space of (B-cc, B...

GEOMETRIC-QUANTIZATION | DEFORMATION QUANTIZATION | NILPOTENT ORBITS | EQUATIONS | PHYSICS, MATHEMATICAL | SIMONS GAUGE-THEORY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

GEOMETRIC-QUANTIZATION | DEFORMATION QUANTIZATION | NILPOTENT ORBITS | EQUATIONS | PHYSICS, MATHEMATICAL | SIMONS GAUGE-THEORY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

1992, 2nd ed., Oxford mathematical monographs., ISBN 0198536739, xi, 307

Book

IEEE transactions on communications, ISSN 1558-0857, 2019, Volume 67, Issue 10, pp. 6796 - 6815

.... The Bussgang decomposition is used to model the effect of quantization. The max-min problem is studied, where the minimum rate...

Fading channels | Quantization (signal) | generalized eigenvalue | limited fronthaul | Channel estimation | Receivers | geometric programming | Cell-free Massive MIMO | Resource management | Uplink | OPTIMIZATION | TELECOMMUNICATIONS | SINR | EFFICIENCY | ENGINEERING, ELECTRICAL & ELECTRONIC

Fading channels | Quantization (signal) | generalized eigenvalue | limited fronthaul | Channel estimation | Receivers | geometric programming | Cell-free Massive MIMO | Resource management | Uplink | OPTIMIZATION | TELECOMMUNICATIONS | SINR | EFFICIENCY | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Annals of physics, ISSN 0003-4916, 2015, Volume 363, Issue Complete, pp. 253 - 261

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an...

Persistent currents | Aharonov–Anandan phase | Landau quantization | Scalar Aharonov–Bohm effect | Magnetic quadrupole moment | Geometric phase | Scalar Aharonov-Bohm effect | Aharonov-Anandan phase | SPACE | NONDISPERSIVE PHASE | ANALOG | PHYSICS, MULTIDISCIPLINARY | ELECTRIC-DIPOLE MOMENT | MASS | Quantum theory | QUADRUPOLE MOMENTS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | NEUTRAL PARTICLES | SCALARS | MAGNETIC MOMENTS | POTENTIALS | ENERGY LEVELS | QUANTIZATION | AHARONOV-BOHM EFFECT | WAVE FUNCTIONS

Persistent currents | Aharonov–Anandan phase | Landau quantization | Scalar Aharonov–Bohm effect | Magnetic quadrupole moment | Geometric phase | Scalar Aharonov-Bohm effect | Aharonov-Anandan phase | SPACE | NONDISPERSIVE PHASE | ANALOG | PHYSICS, MULTIDISCIPLINARY | ELECTRIC-DIPOLE MOMENT | MASS | Quantum theory | QUADRUPOLE MOMENTS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | NEUTRAL PARTICLES | SCALARS | MAGNETIC MOMENTS | POTENTIALS | ENERGY LEVELS | QUANTIZATION | AHARONOV-BOHM EFFECT | WAVE FUNCTIONS

Journal Article

1980, Oxford mathematical monographs, ISBN 9780198535287, xi, 316

Book

Classical and Quantum Gravity, ISSN 0264-9381, 12/2015, Volume 32, Issue 24, pp. 245009 - 245028

We study the Fock quantization of a compound classical system consisting of point masses and a scalar field...

QFT in curved spacetimes | Fock quantization | geometric Hamiltonian formulation | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | QFT in curved space-times | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Quantization | Scalars | Hilbert space | Mathematical models | Equations of motion | Quantum gravity | Geometric constraints

QFT in curved spacetimes | Fock quantization | geometric Hamiltonian formulation | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | QFT in curved space-times | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Quantization | Scalars | Hilbert space | Mathematical models | Equations of motion | Quantum gravity | Geometric constraints

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 10/2016, Volume 26, Issue 4, pp. 2664 - 2710

.... A comparison with the spin-c Dirac quantization is also included.

Symplectic compact manifold | Geometric quantization | Berezin–Toeplitz operators | Semiclassical limit | Spin-c Dirac operator | KAHLER-MANIFOLDS | MATHEMATICS | SOMMERFELD-LAGRANGIAN SUBMANIFOLDS | BERGMAN-KERNEL | TOEPLITZ-OPERATORS | ASYMPTOTICS | LINE BUNDLES | Berezin-Toeplitz operators

Symplectic compact manifold | Geometric quantization | Berezin–Toeplitz operators | Semiclassical limit | Spin-c Dirac operator | KAHLER-MANIFOLDS | MATHEMATICS | SOMMERFELD-LAGRANGIAN SUBMANIFOLDS | BERGMAN-KERNEL | TOEPLITZ-OPERATORS | ASYMPTOTICS | LINE BUNDLES | Berezin-Toeplitz operators

Journal Article

Journal of mathematical physics, ISSN 1089-7658, 2018, Volume 59, Issue 8, p. 082103

We define mixed states associated with submanifolds with probability densities in quantizable closed Kähler manifolds. Then, we address the problem of...

SYMPLECTIC-MANIFOLDS | PHYSICS, MATHEMATICAL | TOEPLITZ-OPERATORS | Upper bounds | Manifolds (mathematics)

SYMPLECTIC-MANIFOLDS | PHYSICS, MATHEMATICAL | TOEPLITZ-OPERATORS | Upper bounds | Manifolds (mathematics)

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 06/2012, Volume 62, Issue 6, pp. 1373 - 1396

We present a rigorous and functorial quantization scheme for affine field theories, i.e...

Feynman path integral | General boundary formulation | Geometric quantization | Quantum field theory | Topological quantum field theory | Coherent states | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Feynman path integral | General boundary formulation | Geometric quantization | Quantum field theory | Topological quantum field theory | Coherent states | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2015, Volume 282, pp. 362 - 426

We formulate a quantization commutes with reduction principle in the setting where the Lie group G, the symplectic manifold it acts on, and the orbit space of the action may all be...

Locally compact groups | Geometric quantization | Hamiltonian manifold | Hochs–Landsman conjecture | Analytic localization | Guillemin–Sternberg conjecture | Witten deformation | Momentum map | Dirac operator | Family of inner products | Guillemin-Sternberg conjecture | Hochs-Landsman conjecture | PROPER MOMENT MAPS | INDEX THEOREM | SPACES | GUILLEMIN-STERNBERG | MULTIPLICITIES | CONJECTURE | MATHEMATICS | REDUCTION | GROUP-REPRESENTATIONS | MANIFOLDS | Algebra

Locally compact groups | Geometric quantization | Hamiltonian manifold | Hochs–Landsman conjecture | Analytic localization | Guillemin–Sternberg conjecture | Witten deformation | Momentum map | Dirac operator | Family of inner products | Guillemin-Sternberg conjecture | Hochs-Landsman conjecture | PROPER MOMENT MAPS | INDEX THEOREM | SPACES | GUILLEMIN-STERNBERG | MULTIPLICITIES | CONJECTURE | MATHEMATICS | REDUCTION | GROUP-REPRESENTATIONS | MANIFOLDS | Algebra

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2011, Volume 253, Issue 1, pp. 169 - 211

We study the formal geometric quantization of noncompact Hamiltonian manifolds. Our main result is that two quantization processes coincide...

Reduction | Moment map | Transversally elliptic symbol | Geometric quantization | MATHEMATICS | transversally elliptic symbol | EQUIVARIANT INDEX | moment map | CHARACTER | reduction | geometric quantization | ELLIPTIC-OPERATORS | MULTIPLICITIES | CUTS | SYMPLECTIC REDUCTION

Reduction | Moment map | Transversally elliptic symbol | Geometric quantization | MATHEMATICS | transversally elliptic symbol | EQUIVARIANT INDEX | moment map | CHARACTER | reduction | geometric quantization | ELLIPTIC-OPERATORS | MULTIPLICITIES | CUTS | SYMPLECTIC REDUCTION

Journal Article

Kyoto Journal of Mathematics, ISSN 2156-2261, 12/2018, Volume 58, Issue 4, pp. 695 - 864

We give a global, intrinsic, and coordinate-free quantization formalism for Gromov-Witten invariants and their B-model counterparts, which simultaneously generalizes the quantization formalisms...

MATHEMATICS | FROBENIUS STRUCTURES | TOPOLOGICAL STRINGS | COHOMOLOGY | HYPERSURFACES | SYSTEMS | LEFSCHETZ | GROMOV-WITTEN INVARIANTS | QUANTUM RIEMANN-ROCH | MIRROR SYMMETRY | CONJECTURE

MATHEMATICS | FROBENIUS STRUCTURES | TOPOLOGICAL STRINGS | COHOMOLOGY | HYPERSURFACES | SYSTEMS | LEFSCHETZ | GROMOV-WITTEN INVARIANTS | QUANTUM RIEMANN-ROCH | MIRROR SYMMETRY | CONJECTURE

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 09/2017, Volume 119, pp. 286 - 303

... of Kähler polarizations parametrized by the upper half plane S. Using this family, geometric quantization, including the half-form correction, produces the field Hcorr...

Adapted complex structures | Geometric quantization | Hilbert fields | MATHEMATICS, APPLIED | LIE-GROUPS | GEOMETRIC-QUANTIZATION | TRANSFORM | MANIFOLDS | PHYSICS, MATHEMATICAL | ROOT SYSTEMS | MONGE-AMPERE EQUATION | HYPERGEOMETRIC-FUNCTIONS

Adapted complex structures | Geometric quantization | Hilbert fields | MATHEMATICS, APPLIED | LIE-GROUPS | GEOMETRIC-QUANTIZATION | TRANSFORM | MANIFOLDS | PHYSICS, MATHEMATICAL | ROOT SYSTEMS | MONGE-AMPERE EQUATION | HYPERGEOMETRIC-FUNCTIONS

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 05/2005, Volume 17, Issue 4, pp. 391 - 490

This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom...

Berezin quantization | Bereziu Touplitz quantization | Deformation quantization | Geometric quantization | Coherent state quantization | Canonical quantization | Borel quantization | borel quantization | canonical quantization | GEOMETRIC-QUANTIZATION | DIFFEOMORPHISM-GROUPS | PHYSICS, MATHEMATICAL | ORDERING PROBLEM | Berezin-Toeplitz quantization | QUANTUM RIEMANN SURFACES | COHERENT-STATE REPRESENTATIONS | deformation quantization | HARMONIC-ANALYSIS | coherent state quantization | TOEPLITZ QUANTIZATION | PHASE-SPACE REDUCTION | geometric quantization | Physicists | Methods

Berezin quantization | Bereziu Touplitz quantization | Deformation quantization | Geometric quantization | Coherent state quantization | Canonical quantization | Borel quantization | borel quantization | canonical quantization | GEOMETRIC-QUANTIZATION | DIFFEOMORPHISM-GROUPS | PHYSICS, MATHEMATICAL | ORDERING PROBLEM | Berezin-Toeplitz quantization | QUANTUM RIEMANN SURFACES | COHERENT-STATE REPRESENTATIONS | deformation quantization | HARMONIC-ANALYSIS | coherent state quantization | TOEPLITZ QUANTIZATION | PHASE-SPACE REDUCTION | geometric quantization | Physicists | Methods

Journal Article

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