Classical and Quantum Gravity, ISSN 0264-9381, 05/2015, Volume 32, Issue 9, pp. 95005 - 95054

We consider the De Donder-Weyl (DW) Hamiltonian formulation of the Palatini action of vielbein gravity formulated in terms of the solder form and spin connection, which are treated as independent variables...

Geometry | De Donder-Weyl | Palatini gravity | Multisymplectic | Vielbein gravity | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | SPIN STRUCTURES | CLASSICAL FIELD-THEORY | ASHTEKAR VARIABLES | CANONICAL STRUCTURE | GAUGE-NATURAL BUNDLES | L-INFINITY-ALGEBRAS | QUANTIZED-FIELDS | SYMPLECTIC APPROACH | POISSON BRACKET | vielbein gravity | ASTRONOMY & ASTROPHYSICS | multisymplectic geometry | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Construction | Solders | Brackets | Mathematical analysis | Independent variables | Quantum gravity | General Relativity and Quantum Cosmology | Mathematics | Mathematical Physics | Physics

Geometry | De Donder-Weyl | Palatini gravity | Multisymplectic | Vielbein gravity | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | SPIN STRUCTURES | CLASSICAL FIELD-THEORY | ASHTEKAR VARIABLES | CANONICAL STRUCTURE | GAUGE-NATURAL BUNDLES | L-INFINITY-ALGEBRAS | QUANTIZED-FIELDS | SYMPLECTIC APPROACH | POISSON BRACKET | vielbein gravity | ASTRONOMY & ASTROPHYSICS | multisymplectic geometry | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Construction | Solders | Brackets | Mathematical analysis | Independent variables | Quantum gravity | General Relativity and Quantum Cosmology | Mathematics | Mathematical Physics | Physics

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 11/2017, Volume 34, Issue 23, p. 235002

...) under the De Donder-Weyl Hamiltonian formulation. The field equations, known in this formalism as the De Donder- Weyl equations, are obtained by means of the graded Poisson-Gerstenhaber bracket structure present within the De Donder-Weyl formulation...

gravity | Poisson-Gerstenhaber bracket | gauge theory | Hamiltonian | De Donder-Weyl equations | Einstein equat | polysymplectic formalism | SUPERGRAVITY | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | CALCULUS | Einstein equations | ASTRONOMY & ASTROPHYSICS | VARIABLES | PRECANONICAL QUANTIZATION | GAUGE | GEOMETRY | PHYSICS, PARTICLES & FIELDS

gravity | Poisson-Gerstenhaber bracket | gauge theory | Hamiltonian | De Donder-Weyl equations | Einstein equat | polysymplectic formalism | SUPERGRAVITY | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | CALCULUS | Einstein equations | ASTRONOMY & ASTROPHYSICS | VARIABLES | PRECANONICAL QUANTIZATION | GAUGE | GEOMETRY | PHYSICS, PARTICLES & FIELDS

Journal Article

CLASSICAL AND QUANTUM GRAVITY, ISSN 0264-9381, 06/2019, Volume 36, Issue 11, p. 115003

... naturally emerge by solving the simplicity constraints of the theory. Further, from the polysymplectic analysis of the CMPR action the De Donder-Weyl Hamiltonian...

Immirzi parameter | FIELDS | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | CALCULUS | polysymplectic formalism | BF gravity | Einstein equations | De Donder-Weyl theory | Poisson-Gerstenhaber bracket | ASTRONOMY & ASTROPHYSICS | PRECANONICAL QUANTIZATION | PHYSICS, PARTICLES & FIELDS

Immirzi parameter | FIELDS | QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | CALCULUS | polysymplectic formalism | BF gravity | Einstein equations | De Donder-Weyl theory | Poisson-Gerstenhaber bracket | ASTRONOMY & ASTROPHYSICS | PRECANONICAL QUANTIZATION | PHYSICS, PARTICLES & FIELDS

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 06/2017, Volume 32, Issue 17, p. 1750101

We analyze the De Donder–Weyl covariant field equations for the topologically massive Yang–Mills theory...

De Donder-Weyl Hamiltonian | Yang-Mills | Gauge theory | polysymplectic formulation | Poisson-Gerstenhaber bracket | Chern-Simons | SIMONS | PHYSICS, NUCLEAR | QUANTIZATION | PHYSICS, PARTICLES & FIELDS

De Donder-Weyl Hamiltonian | Yang-Mills | Gauge theory | polysymplectic formulation | Poisson-Gerstenhaber bracket | Chern-Simons | SIMONS | PHYSICS, NUCLEAR | QUANTIZATION | PHYSICS, PARTICLES & FIELDS

Journal Article

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SchrÖdinger Wave Functional in Quantum Yang–Mills Theory from Precanonical Quantization

Reports on Mathematical Physics, ISSN 0034-4877, 12/2018, Volume 82, Issue 3, pp. 373 - 388

A relation between the precanonical quantization of pure Yang–Mills fields and the standard functional Schrödinger representation in the temporal gauge is...

precanonical quantization | quantum Yang–Mills theory | De Donder-Weyl formalism | canonical quantization | Gauss constraint | Volterra product integral | Clifford algebra | functional Schrödinger representation | COULOMB | FIELDS | quantum Yang-Mills theory | WEYL | PHYSICS, MATHEMATICAL | EQUIVALENCE | SPACE | functional Schrodinger representation | MECHANICS | COVARIANT | REGULARIZATION | GAUGE

precanonical quantization | quantum Yang–Mills theory | De Donder-Weyl formalism | canonical quantization | Gauss constraint | Volterra product integral | Clifford algebra | functional Schrödinger representation | COULOMB | FIELDS | quantum Yang-Mills theory | WEYL | PHYSICS, MATHEMATICAL | EQUIVALENCE | SPACE | functional Schrodinger representation | MECHANICS | COVARIANT | REGULARIZATION | GAUGE

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 09/2017, Volume 14, Issue 9

The spectrum of masses of the colorless states of DW Hamiltonian operator of quantum SU(2) Yang-Mills field theory on R-D obtained via the precanonical...

eigenvalues | precanonical quantization | De Donder-Weyl formalism | mass gap | Airy function | Clifford analysis | discrete spectrum | Quantum Yang-Mills theory | Schrödinger operators | MECHANICS | Schrodinger operators | REPRESENTATION | PHYSICS, MATHEMATICAL

eigenvalues | precanonical quantization | De Donder-Weyl formalism | mass gap | Airy function | Clifford analysis | discrete spectrum | Quantum Yang-Mills theory | Schrödinger operators | MECHANICS | Schrodinger operators | REPRESENTATION | PHYSICS, MATHEMATICAL

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 2018, Volume 16, Issue 2

... system obtained by the precanonical quantization based on the space-time symmetric De Donder-Weyl Hamiltonian theory...

precanonical quantization | canonical quantization | De Donder-Weyl formalism | Clifford algebra | product integral | functional Schrödinger representation | Quantum field theory in curved space-time | functional Schrodinger representation | VACUUM STATES | CALCULUS | COVARIANT HAMILTONIAN-FORMALISM | PHYSICS, MATHEMATICAL

precanonical quantization | canonical quantization | De Donder-Weyl formalism | Clifford algebra | product integral | functional Schrödinger representation | Quantum field theory in curved space-time | functional Schrodinger representation | VACUUM STATES | CALCULUS | COVARIANT HAMILTONIAN-FORMALISM | PHYSICS, MATHEMATICAL

Journal Article

International Journal of Modern Physics E, ISSN 0218-3013, 07/2016, Volume 25, Issue 7, p. 1642005

Electromagnetism, the strong and the weak interactions are commonly formulated as gauge theories in a Lagrangian description. In this paper, we present an...

canonical transformation | Gauge theory | de Donder-Weyl theory | field theory | Hamilton formalism | scalar electrodynamics | FIELD-THEORY | CALCULUS | PHYSICS, NUCLEAR | FORMALISM | PHYSICS, PARTICLES & FIELDS

canonical transformation | Gauge theory | de Donder-Weyl theory | field theory | Hamilton formalism | scalar electrodynamics | FIELD-THEORY | CALCULUS | PHYSICS, NUCLEAR | FORMALISM | PHYSICS, PARTICLES & FIELDS

Journal Article

Annals of Physics, ISSN 0003-4916, 03/2020, Volume 414, p. 168092

We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of k-contact...

[formula omitted]-symplectic structure | Burgers’ equation | Contact structure | De Donder–Weyl theory | Hamiltonian field theory | System with dissipation | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | De Donder-Weyl theory | Burgers' equation | k-symplectic structure

[formula omitted]-symplectic structure | Burgers’ equation | Contact structure | De Donder–Weyl theory | Hamiltonian field theory | System with dissipation | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | De Donder-Weyl theory | Burgers' equation | k-symplectic structure

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2013, Volume 1514, Issue 1, pp. 73 - 76

The basics of precanonical quantization and its relation to the functional Schro[Dot]dinger picture in QFT are briefly outlined. The approach is then applied...

quantum cosmology | precanonical quantization | spin connection | tetrad gravity | De Donder-Weyl theory | quantum gravity | Gravitation | Mathematical analysis | Flats | Quantization | Cosmology | Universe | Mathematical models | Joints | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SCHROEDINGER EQUATION | SPIN | TRANSITION AMPLITUDES | EINSTEIN FIELD EQUATIONS | SCHROEDINGER PICTURE | COSMOLOGY | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | SPACE-TIME | GRAVITATION | QUANTIZATION | QUANTUM FIELD THEORY | UNIVERSE

quantum cosmology | precanonical quantization | spin connection | tetrad gravity | De Donder-Weyl theory | quantum gravity | Gravitation | Mathematical analysis | Flats | Quantization | Cosmology | Universe | Mathematical models | Joints | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SCHROEDINGER EQUATION | SPIN | TRANSITION AMPLITUDES | EINSTEIN FIELD EQUATIONS | SCHROEDINGER PICTURE | COSMOLOGY | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | SPACE-TIME | GRAVITATION | QUANTIZATION | QUANTUM FIELD THEORY | UNIVERSE

Conference Proceeding

Journal of Geometric Mechanics, ISSN 1941-4889, 03/2012, Volume 4, Issue 1, pp. 1 - 26

.... Using this triple, we prove that Euler-Lagrange and Hamilton-De Donder-Weyl equations are the local equations defining Lagrangian submanifolds...

Hamilton-De Donder-Weyl equation | MATHEMATICS, APPLIED | multisymplectic structure | MAPS | Lagrangian submanifold | EQUATIONS | SYSTEMS | Field theory | Tulczyjew's triple | Euler-Lagrange equation | PHYSICS, MATHEMATICAL | GEOMETRY

Hamilton-De Donder-Weyl equation | MATHEMATICS, APPLIED | multisymplectic structure | MAPS | Lagrangian submanifold | EQUATIONS | SYSTEMS | Field theory | Tulczyjew's triple | Euler-Lagrange equation | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

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Polysymplectic integrator for the Short Pulse Equation and numerical general relativity

14th Marcel Grossman Meeting On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, Proceedings, 2018, pp. 2677 - 2682

Conference Proceeding

Reports on Mathematical Physics, ISSN 0034-4877, 2004, Volume 53, Issue 2, pp. 181 - 193

Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW...

Functional Schrödinger representation | Mass gap | De Donder-Weyl formalism | Magnetic opreator | Yang-Mills theory | Precanonical quantization | Clifford algebra

Functional Schrödinger representation | Mass gap | De Donder-Weyl formalism | Magnetic opreator | Yang-Mills theory | Precanonical quantization | Clifford algebra

Journal Article

SYMMETRY-BASEL, ISSN 2073-8994, 11/2019, Volume 11, Issue 11, p. 1413

The functional Schrodinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the...

precanonical quantization | functional Schrodinger representation | canonical quantization | SYMPLECTIC-GEOMETRY | VACUUM STATES | CALCULUS | MULTIDISCIPLINARY SCIENCES | quantum field theory in curved space-time | COVARIANT HAMILTONIAN-FORMALISM | QUANTIZATION | FORMULATION | De Donder-Weyl Hamiltonian formalism | de donder-weyl hamiltonian formalism | functional schrödinger representation

precanonical quantization | functional Schrodinger representation | canonical quantization | SYMPLECTIC-GEOMETRY | VACUUM STATES | CALCULUS | MULTIDISCIPLINARY SCIENCES | quantum field theory in curved space-time | COVARIANT HAMILTONIAN-FORMALISM | QUANTIZATION | FORMULATION | De Donder-Weyl Hamiltonian formalism | de donder-weyl hamiltonian formalism | functional schrödinger representation

Journal Article

Nonlinear Phenomena in Complex Systems, ISSN 1561-4085, 2014, Volume 17, Issue 4, pp. 372 - 376

Journal Article

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On the “spin connection foam” picture of quantum gravity from precanonical quantization

14th Marcel Grossman Meeting On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, Proceedings, 2018, pp. 3907 - 3915

Conference Proceeding

Reports on Mathematical Physics, ISSN 0034-4877, 1998, Volume 41, Issue 1, pp. 49 - 90

Canonical structure of classical field theory in n dimensions is studied within the covariant polymomentum Hamiltonian formulation of De Donder-Weyl (DW). The bi-vertical ( n + 1...

Classical field theory | multivector fields | Schouten-Nijenhuis bracket | Poincaré-Cartan form | De Donder-Weyle theory | polysymplectic form | Gerstenhaber algebra | Poisson bracket | differential forms | Hamiltonian formalism | De Donder-Weyl theory | Differential forms | Polysymplectic form | Multivector fields | STRINGS | HAMILTONIAN-FORMALISM | Poincare-Cartan form | PHYSICS, MATHEMATICAL | classical field theory | GEOMETRY

Classical field theory | multivector fields | Schouten-Nijenhuis bracket | Poincaré-Cartan form | De Donder-Weyle theory | polysymplectic form | Gerstenhaber algebra | Poisson bracket | differential forms | Hamiltonian formalism | De Donder-Weyl theory | Differential forms | Polysymplectic form | Multivector fields | STRINGS | HAMILTONIAN-FORMALISM | Poincare-Cartan form | PHYSICS, MATHEMATICAL | classical field theory | GEOMETRY

Journal Article

14th Marcel Grossman Meeting On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, Proceedings, 2018, pp. 2828 - 2835

Conference Proceeding

19.
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ON HAMILTONIAN FORMULATIONS AND CONSERVATION LAWS FOR PLATE THEORIES OF VEKUA-AMOSOV TYPE

International Journal for Computational Civil and Structural Engineering, ISSN 2587-9618, 12/2017, Volume 13, Issue 4, pp. 82 - 95

.... The infinite dimensional formulation with one evolution variable, or an “instantaneous” formalism, as well as the de Donder...

refined shell theory, analytical mechanics of continua, Hamiltonian formalism, de Donder – Weyl formulation, conservation laws

refined shell theory, analytical mechanics of continua, Hamiltonian formalism, de Donder – Weyl formulation, conservation laws

Journal Article

Journal of Geometry and Symmetry in Physics, ISSN 1312-5192, 2015, Volume 37, pp. 43 - 66

J. Geom. Symmetry Phys. 37 (2015) 43-66 We discuss the precanonical quantization of fields which is based on the De Donder--Weyl (DW...

Curved space-time | Schrödinger functional | De Donder-Weyl theory | Yang-Mills theory | Precanonical quantization | Clifford algebra | Polysymplectic structure | Quantum field theory

Curved space-time | Schrödinger functional | De Donder-Weyl theory | Yang-Mills theory | Precanonical quantization | Clifford algebra | Polysymplectic structure | Quantum field theory

Journal Article

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