2005, illustrated edition, Oxford graduate texts, ISBN 9780198567264, Volume 9780198567264, xx, 597

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to...

Mechanics, Analytic | Physics | Science | Quantum theory | Hamiltonian theory | Dirac's formalism | Lorenz transformation | Classical mechanics | Special relativity | Quantum mechanics | Dyadics | Analytical mechanics | Newtonian physics | Relativistic mechanics

Mechanics, Analytic | Physics | Science | Quantum theory | Hamiltonian theory | Dirac's formalism | Lorenz transformation | Classical mechanics | Special relativity | Quantum mechanics | Dyadics | Analytical mechanics | Newtonian physics | Relativistic mechanics

Book

Theoretical Chemistry Accounts, ISSN 1432-881X, 1/2012, Volume 131, Issue 1, pp. 1 - 20

It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing molecules....

X2C method | Theoretical and Computational Chemistry | Chemistry | Relativistic electronic structure theory | Picture change error | Physical Chemistry | Douglas–Kroll–Hess method | Fock operator | Atomic/Molecular Structure and Spectra | Inorganic Chemistry | Organic Chemistry | Douglas-Kroll-Hess method | DIRAC-EQUATION | DENSITY-FUNCTIONAL CALCULATIONS | CHEMISTRY, PHYSICAL | REGULAR APPROXIMATION | NORMALIZED ELIMINATION | QUANTUM-CHEMISTRY | DOUGLAS-KROLL TRANSFORMATION | NONRELATIVISTIC METHODS | PROJECTION OPERATORS | HESS TRANSFORMATION | ELECTRON-DENSITY

X2C method | Theoretical and Computational Chemistry | Chemistry | Relativistic electronic structure theory | Picture change error | Physical Chemistry | Douglas–Kroll–Hess method | Fock operator | Atomic/Molecular Structure and Spectra | Inorganic Chemistry | Organic Chemistry | Douglas-Kroll-Hess method | DIRAC-EQUATION | DENSITY-FUNCTIONAL CALCULATIONS | CHEMISTRY, PHYSICAL | REGULAR APPROXIMATION | NORMALIZED ELIMINATION | QUANTUM-CHEMISTRY | DOUGLAS-KROLL TRANSFORMATION | NONRELATIVISTIC METHODS | PROJECTION OPERATORS | HESS TRANSFORMATION | ELECTRON-DENSITY

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2014, Volume 36, Issue 4, pp. A1581 - A1608

In lattice quantum chromodynamics (QCD) computations a substantial amount of work is spent in solving discretized versions of the Dirac equation. Conventional...

Aggregation | Adaptivity | Parallel computing | Multigrid | Multilevel | Lattice qcd | Domain decomposition | Wilson-Dirac operator | MATHEMATICS, APPLIED | ALPHA-SA | domain decomposition | multilevel | multigrid | aggregation | KRYLOV SUBSPACE METHODS | adaptivity | QCD | MASS | parallel computing | lattice QCD | Algebra | Computation | Lattices | Dirac equation | Solvers | Mathematical models | Quantum chromodynamics

Aggregation | Adaptivity | Parallel computing | Multigrid | Multilevel | Lattice qcd | Domain decomposition | Wilson-Dirac operator | MATHEMATICS, APPLIED | ALPHA-SA | domain decomposition | multilevel | multigrid | aggregation | KRYLOV SUBSPACE METHODS | adaptivity | QCD | MASS | parallel computing | lattice QCD | Algebra | Computation | Lattices | Dirac equation | Solvers | Mathematical models | Quantum chromodynamics

Journal Article

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 09/2009, Volume 80, Issue 5

A new quark-field smearing algorithm is defined which enables efficient calculations of a broad range of hadron correlation functions. The technique applies a...

FERMIONS | MATRIX | GAUGE-THEORY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Lattice | CORRELATION FUNCTIONS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | QUANTUM CHROMODYNAMICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CONSTRUCTION | QUARKS | ALGORITHMS | DIRAC OPERATORS | PHYSICS | CREATION OPERATORS | HADRONS | PROPAGATOR

FERMIONS | MATRIX | GAUGE-THEORY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Lattice | CORRELATION FUNCTIONS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | QUANTUM CHROMODYNAMICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CONSTRUCTION | QUARKS | ALGORITHMS | DIRAC OPERATORS | PHYSICS | CREATION OPERATORS | HADRONS | PROPAGATOR

Journal Article

2018, Springer Monographs in Mathematics, ISBN 3030021246, 324

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and...

eBook

Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2018, Volume 28, Issue 1, pp. 1 - 19

This is the second part in a series of two papers. The k-Dirac complex is a complex of differential operators which are naturally associated to a particular...

Secondary 58A20 | Mathematical Methods in Physics | 58J10 | k-Dirac operator | Theoretical, Mathematical and Computational Physics | k-Dirac complex | Resolution of overdetermined system | Primary 35N05 | Applications of Mathematics | Physics, general | Invariant differential complexes | Physics | MATHEMATICS, APPLIED | COMPLEX | CARTAN-KAHLER THEOREM | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

Secondary 58A20 | Mathematical Methods in Physics | 58J10 | k-Dirac operator | Theoretical, Mathematical and Computational Physics | k-Dirac complex | Resolution of overdetermined system | Primary 35N05 | Applications of Mathematics | Physics, general | Invariant differential complexes | Physics | MATHEMATICS, APPLIED | COMPLEX | CARTAN-KAHLER THEOREM | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry

Journal Article

Physical Review Letters, ISSN 0031-9007, 10/2010, Volume 105, Issue 16, p. 162002

We calculate the leading contribution to the spectral density of the Wilson Dirac operator using chiral perturbation theory where volume and lattice spacing...

PHASE-STRUCTURE | LATTICE QCD | STATES | PHYSICS, MULTIDISCIPLINARY | QUARKS | FERMIONS | LIMIT | CORRECTIONS | RANDOMNESS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SPECTRAL DENSITY | WILSON LOOP | MATHEMATICAL OPERATORS | DIRAC OPERATORS | FUNCTIONS | PARTICLE PROPERTIES | GAUGE INVARIANCE | FIELD THEORIES | CONSTRUCTIVE FIELD THEORY | MATRICES | QUANTUM OPERATORS | LATTICE FIELD THEORY | PERTURBATION THEORY | INVARIANCE PRINCIPLES | CHIRALITY | QUANTUM FIELD THEORY | SPECTRAL FUNCTIONS

PHASE-STRUCTURE | LATTICE QCD | STATES | PHYSICS, MULTIDISCIPLINARY | QUARKS | FERMIONS | LIMIT | CORRECTIONS | RANDOMNESS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SPECTRAL DENSITY | WILSON LOOP | MATHEMATICAL OPERATORS | DIRAC OPERATORS | FUNCTIONS | PARTICLE PROPERTIES | GAUGE INVARIANCE | FIELD THEORIES | CONSTRUCTIVE FIELD THEORY | MATRICES | QUANTUM OPERATORS | LATTICE FIELD THEORY | PERTURBATION THEORY | INVARIANCE PRINCIPLES | CHIRALITY | QUANTUM FIELD THEORY | SPECTRAL FUNCTIONS

Journal Article

International Journal of Modern Physics D, ISSN 0218-2718, 12/2014, Volume 23, Issue 14, pp. 1444003 - 1-1444003-9

In this paper, we provide a new derivation of the Dirac equation which promptly generalizes to higher spins. We apply this idea to spin-half Elko dark matter.

Dirac operator | kinematics | ELKO | SPINOR FIELDS | ASTRONOMY & ASTROPHYSICS | Derivation | Operators | Dark matter | Parity | Dirac equation

Dirac operator | kinematics | ELKO | SPINOR FIELDS | ASTRONOMY & ASTROPHYSICS | Derivation | Operators | Dark matter | Parity | Dirac equation

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2019, Volume 293, Issue 1, pp. 485 - 502

We re-visit the eigenvalue estimate of the Dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal Laplace operator as...

Poincare–Einstein metric | Eigenvalue | Yamabe invariant | Mathematics, general | Mathematics | Dirac operator | Boundary condition | MATHEMATICS | CONSTANT MEAN-CURVATURE | CONFORMAL DEFORMATION | BOUNDARY-VALUE-PROBLEMS | MANIFOLDS | SPECTRAL ASYMMETRY | Poincare-Einstein metric

Poincare–Einstein metric | Eigenvalue | Yamabe invariant | Mathematics, general | Mathematics | Dirac operator | Boundary condition | MATHEMATICS | CONSTANT MEAN-CURVATURE | CONFORMAL DEFORMATION | BOUNDARY-VALUE-PROBLEMS | MANIFOLDS | SPECTRAL ASYMMETRY | Poincare-Einstein metric

Journal Article

New Journal of Physics, ISSN 1367-2630, 2014, Volume 16, Issue 4, pp. 43012 - 9

Although the spin is regarded as a fundamental property of the electron, there is no universally accepted spin operator within the framework of relativistic...

hydrogen-like ions | relativistic quantum mechanics | spin | DIRAC PARTICLE | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | MOMENTUM | FIELD | SYSTEMS | STATE | POSITION OPERATORS | POLARIZATION | Operators (mathematics) | Hydrogen storage | Quantum mechanics | Angular momentum | Relativism | Electron spin | Relativistic effects | Operators | Charging | Algebra | Ground state | Proposals

hydrogen-like ions | relativistic quantum mechanics | spin | DIRAC PARTICLE | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | MOMENTUM | FIELD | SYSTEMS | STATE | POSITION OPERATORS | POLARIZATION | Operators (mathematics) | Hydrogen storage | Quantum mechanics | Angular momentum | Relativism | Electron spin | Relativistic effects | Operators | Charging | Algebra | Ground state | Proposals

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 01/2019, Volume 87, pp. 172 - 178

Given the spectrum of the Dirac operator, together with the potential on the half-interval and one boundary condition, this paper provides reconstruction of...

Reconstruction | Dirac operator | Solvability | Hochstadt–Lieberman theorem | MATHEMATICS, APPLIED | Hochstadt-Lieberman theorem | SCHRODINGER

Reconstruction | Dirac operator | Solvability | Hochstadt–Lieberman theorem | MATHEMATICS, APPLIED | Hochstadt-Lieberman theorem | SCHRODINGER

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 07/2014, Volume 31, Issue 13, p. 135015

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the...

Symmetry operators | Killing spinors | Massless fields | Maxwell equation | Dirac-Weyl equation | FIELDS | SPIN | PHYSICS, MULTIDISCIPLINARY | DIRAC-EQUATION | massless fields | CONSERVED-CURRENTS | ASTRONOMY & ASTROPHYSICS | maxwell equation | VARIABLES | CURVED SPACE-TIME | SEPARATION | symmetry operators | PHYSICS, PARTICLES & FIELDS | Manifolds | Descriptions | Operators | Mathematical analysis | Quantum gravity | Computer programs | Symmetry

Symmetry operators | Killing spinors | Massless fields | Maxwell equation | Dirac-Weyl equation | FIELDS | SPIN | PHYSICS, MULTIDISCIPLINARY | DIRAC-EQUATION | massless fields | CONSERVED-CURRENTS | ASTRONOMY & ASTROPHYSICS | maxwell equation | VARIABLES | CURVED SPACE-TIME | SEPARATION | symmetry operators | PHYSICS, PARTICLES & FIELDS | Manifolds | Descriptions | Operators | Mathematical analysis | Quantum gravity | Computer programs | Symmetry

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2020, Volume 485, Issue 2, p. 123808

The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze...

Fermionic signature operator | de Sitter spacetime | Hadamard states | Dirac operator | Quantum field theory on curved spacetime | MATHEMATICS, APPLIED | STATES | TIMES | NONPERTURBATIVE CONSTRUCTION | QUANTUM-FIELD-THEORY | MATHEMATICS | HADAMARD CONDITION | PROJECTOR

Fermionic signature operator | de Sitter spacetime | Hadamard states | Dirac operator | Quantum field theory on curved spacetime | MATHEMATICS, APPLIED | STATES | TIMES | NONPERTURBATIVE CONSTRUCTION | QUANTUM-FIELD-THEORY | MATHEMATICS | HADAMARD CONDITION | PROJECTOR

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 930 - 960

We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of...

Operators with an Involution | Spectral asymptotic analysis | Method of similar operators | Dirac operator | Mathematics - Functional Analysis

Operators with an Involution | Spectral asymptotic analysis | Method of similar operators | Dirac operator | Mathematics - Functional Analysis

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 3/2013, Volume 2013, Issue 3, pp. 1 - 34

We discuss the systematic decomposition of the dimension nine neutrinoless double beta decay operator, focusing on mechanisms with potentially small...

Neutrino Physics | Beyond Standard Model | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LEPTOQUARK | SUPERSYMMETRY | SUPERFORMULA | SEARCH | LHC | MASS | LEPTON NUMBER | QUARK | DIRAC | PHYSICS, PARTICLES & FIELDS | Analysis | Resveratrol | Operators | Accessibility | Beta decay | Lists | Neutrinos | Cosmology | Decomposition | Gain | Physics - High Energy Physics - Phenomenology

Neutrino Physics | Beyond Standard Model | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LEPTOQUARK | SUPERSYMMETRY | SUPERFORMULA | SEARCH | LHC | MASS | LEPTON NUMBER | QUARK | DIRAC | PHYSICS, PARTICLES & FIELDS | Analysis | Resveratrol | Operators | Accessibility | Beta decay | Lists | Neutrinos | Cosmology | Decomposition | Gain | Physics - High Energy Physics - Phenomenology

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2016, Volume 440, Issue 1, pp. 155 - 166

In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function...

Dirac operator | Nonlocal conditions | Inverse spectral problems

Dirac operator | Nonlocal conditions | Inverse spectral problems

Journal Article