LIBRARY: Multisymplectic Geometry & Field Theory
Author(s) | Title | References | Year |
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Author(s) | Title | Reference | Year |
Cantrijn, F., Ibort, A., de Leon, M., | On the Geometry of Multisymplectic Manifolds, | J. Austral. Math. Soc., 66, (1999), pp. 303-330 | 1999 |
Carathéodory C., | Variationsrechnung und Partielle Differentialgleichungen erster Ordnung, | Teubner, Leipzig, Reprinted by Chelsea, New York (1982). | 1935 |
Carinena J.F., Crampin M., Ibort L.A., | On the multisymplectic formalism for
first order field theories |
Diff. Geom. Appl. 1 (1991), 345-374. | 1992 |
Dedecker D., | Calcul des variations, formes differentielles et champs geodesiques |
Geometrie differentielle, Colloq. Intern. du CNRS LII, Strasbourg, (1953) 17—34 | 1953 |
Dedecker D., | On the generalization of symplectic geometry to multiple integrals in the calculus of variations, | Differential Geometrical Methods in Mathematical Physics, eds. K. Bleuler and A. Reetz, Lect. Notes Maths. vol. 570, Springer-Verlag, Berlin | 1977 |
De Donder T. | Sur les équations canoniques de Hamilton-Volterra, | Acad. Roy. Belg. Cl. Sci. Meme. | 1911 |
De Donder T. | Théorie Invariante du Calcul des Variations | Nuov. ed. Gauthier-Villars, Paris, | 1935 |
De León M., Salgado M., Vilariño S. | Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches. | ArXiv e-print arXiv:1409.5604 | 2014 |
Forger M., Paufler C., Römer H., | The Poisson bracket for Poisson forms in multisymplectic field theory, | Rev. Math. Phys. {15}, No. 7, arXiv:math-ph/0202043v1. | 2003 |
Forger M., Paufler C., Römer H., | A general construction of Poisson brackets on exact multisymplectic manifolds | Talk delivered at the 34th Symp. on Math. Phys., Torun, Poland, arXiv:math-ph/0208037. | 2002 |
Forger M., Paufler C., Römer H., | Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory | J.Math.Phys. 46, 112901, arXiv:math-ph/0407057. | 2005 |
Forger M., Römer H., | A Poisson Bracket on Multisymplectic Phase Space | Rep. Math. Phys. 48, 211-218, arXiv:math-ph/0009037. | 2001 |
Forger M., Romero S.V., | Covariant Poisson Brackets in Geometric Field Theory | Commun.Math.Phys. 256 (2005) 375-410, arXiv:math-ph/0408008. | 2005 |
Forger M., Gomes L.G., | Multisymplectic and polysymplectic structures on fiber bundles | arXiv:math-ph/0708.1586. | 2007 |
Forger M., Salles M.O., | Hamiltonian Vector Fields on Multiphase Spaces of Classical Field Theory | arXiv:math-ph/1010.0337. | 2010 |
Forger M., Salles M.O., | On Covariant Poisson Brackets in Classical Field Theory | arXiv:math-ph/1501.03780. | 2015 |
García P.L., | Geometría simplética en la teoria de campos, |
Collect. Math. 19, 1-2, 73, | 1968 |
García P.L., | The Poincaré-Cartan invariant in the calculus of variations, |
Symposia Mathematica, Vol. 14 (Convegno di GeometriaSimplettica e Fisica Matematica, INDAM, Rome, 1973), Academic Press, London, 219-246. | 1974 |
García, P.L., Pérez-Rendún | A. Symplectic approach to the theory of quantized fields. I. | Comm. Math. Phys. 13, 24-44, | 1969 |
García, P.L., Pérez-Rendún | Symplectic approach to the theory of quantized fields. II. | Arch. Rational Mech. Anal. 43, 101-124, | 1971 |
Gawedski K., | On the generalization of the canonical formalism in the classical field theory | Rep. Math. Phys. No 4, Vol. 3, 307-326. | 1972 |
Giachetta G., Mangiarotti L., Sardanashvily G. | New Lagrangian and Hamiltonian Methods in Field Theory | World Scientific, Singapore, | 1997 |
Giachetta G., Mangiarotti L., Sardanashvily G. | Polysymplectic Hamiltonian formalism and some quantum outcomes | invited plenary lecture, 9th Int. Conf. Diff. Geom. and its App., Prague, arXiv:hep-th/0411005 | 2004 |
Giachetta G., Mangiarotti L., Sardanashvily G. | Covariant Hamilton equations for field theory. | J. Phys. A {32}, 6629-6642. | 1999 |
Gotay M.J., Isenberg J., Marsden J.E. | Momentum maps and classical relativistic fields, Part I: covariant field theory | arXiv/physics/9801019 | 1998 |
Gotay M.J., Isenberg J., Marsden J.E. | Momentum maps and classical relativistic fields, Part II: Canonical Analysis of Field Theories | arXiv:math-ph/0411032 | 2004 |
Gotay M.J., | A multisymplectic framework for classical field theory and the calculus of variations I. Covariant Hamiltonian formalism, | Mechanics, Analysis, and Geometry: 200 Years After Lagrange (M. Francaviglia, ed.), North Holland, Amsterdam, 203-235. | 1991 |
Gotay M.J., | A multisymplectic framework for classical field theory and the calculus of variations II. Space + time decomposition, Diff. | Geom. Appl., {1}, 375-390. | 1991 |
Gotay M.J., | An exterior differential systems approach to the Cartan form}, in Symplectic | Geometry and Mathematical Physics, eds. P. Donato, C. Duval, e.a. Birkhauser, Boston, 160-188. | 1991 |
Goldschmidt H., Sternberg S. | The Hamilton-Cartan formalism in the calculus of variations | Ann. Inst. Fourier 23. | 1973 |
Günther C., | The polysymplectic Hamiltonian formalism in field theory and the calculus of variations, |
J. Diff. Geom., 25, , 23-53. | 1987 |
Hélein F., | Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory | Contemp. Math. 350, 127147. arXiv:math-ph/0212036 | 2004 |
Hélein F., |
Multisymplectic formalism and the covariant phase space. | in Variational Problems Differential Geometry, R. Bielawski, K. Houston, M. Speight, eds, London Mathematical Society Lecture Note Series 394, Cambridge University Press, p. 94-126. arxiv:1106.2086 | 2012 |
Hélein F., Kouneiher J. | Finite dimensional Hamiltonian formalism for gauge and quantum field theories, | J. Math. Phys. 43, arXiv:math-ph/0004020v3 | 2002 |
Hélein F., Kouneiher J. | Covariant Hamiltonian formalism for the calculus of variations with several variables: Lepage–Dedecker versus De Donder–Weyl, | Adv. Theor. Math. Phys. 8, 565-601 - arXiv:math-ph/0211046 | 2004 |
Hélein F., Kouneiher J. | The notion of observable in the covariant Hamiltonian formalism for the calculus of variations with several variables | arXiv:math-ph/0401047 | 2004 |
Hrabak S.P. | On a Multisymplectic Formulation of the Classical BRST symmetry for First Order Field Theories Part I: Algebraic Structures | arXiv:9901012v1 | 1999 |
Hrabak S.P. | On a Multisymplectic Formulation of the Classical BRST Symmetry for First Order Field Theories Part II: Geometric Structures | arXiv:9901013v1 | 1999 |
Hrabak S.P. | Ambient Diffeomorphism Symmetries of Embedded Submanifolds, Multisymplectic BRST and Pseudoholomorphic Embedding | arXiv:9904026 | 1999 |
Tulczyjew W.M | The graded Lie algebra of multivector fields and the generalized Lie derivative of forms, | Bull. de lAcad. Polon. des Sci., Serie sci. Math., Astr. et Phys. XXII, 937-942. | 1974 |
Tulczyjew W.M., Kijowski J., | A symplectic framework for field theories | Springer-Verlag, Berlin, | 1979 |
Kanatchikov, I.V | Precanonical quantization and the Schrödinger wave functional revisited | Adv. Theor. Math. Phys. 18 (2014) 1249-1265 arXiv:hep-th/1112.5801v4 | 2014 |
Kanatchikov, I.V | On Field Theoretic Generalizations of a Poisson Algebra | Rept.Math.Phys. 40 (1997) 225 arXiv:hep-th/9710069 | 1997 |
Kanatchikov, I.V | Novel algebraic structures from the polysymplectic form in field theory. | Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, vol. 2, eds. H.-D. Doebner e.a. (World Sci., Singapore, 1997) p. 894 arXiv:hep-th/9612255 | 1997 |
Kanatchikov, I.V | Basic structures of the covariant canonical formalism for fields based on the De Donder--Weyl theory. | arXiv:hep-th/9410238 | 1994 |
Kanatchikov, I.V | On the canonical structure of the De Donder-Weyl covariant Hamiltonian formulation of field theory I. Graded Poisson brakets and the equation of motion. | arXiv:hep-th/9312162 | 1993 |
Kanatchikov, I.V | Canonical Structure of Classical Field Theory in the Polymomentum Phase Space | Reports on Mathematical Physics v. 41 No. 1 arXiv:hep-th/9709229 | 1998 |
Kijowski J. | A finite dimensional canonical formalism in the classical field theory | Comm. Math. Phys. 30, 99-128 | 1973 |
Kijowski J., Szczyrba W | A canonical structure for classical field theories, | Commun. Math Phys. 46, 183-206 | 1976 |
Lepage T., | Sur les champs geodesiques du calcul des variations, | Bull. Acad. Roy. Belg., Cl. Sci. 27, 716729, 1036-1046 | 1936 |
Paufler C., | A vertical exterior derivative in multisymplectic geometry and a graded Poisson bracket for nontrivial geometries | Reports on Mathematical Physics 47 (1) 2001, 101-119. arXiv:math-ph/0002032v3 | 2001 |
Paufler C., and Römer H. | Geometry of Hamiltonean n-vectors in Multisymplectic Field Theory | J.Geom.Phys. 44 (2002) 52-69 arXiv:math-ph/0102008v3 | 2002 |
Paufler C. | On The Geometry of Field Theoretic Gerstenhaber Structures | Rept.Math.Phys. 48 (2001) 203-210 arXiv:math-ph/0102012v1 | 2001 |
Paufler C., Römer H. | De Donder-Weyl Equations and Multisymplectic Geometry | Rept.Math.Phys. 49 (2002) 325-334 arXiv:math-ph/0107019 | 2002 |
Zapata J.A. | Observable currents in lattice field theories | arXiv:1602.02304 | 2016 |
Arjang M., Zapata J.A. | Multisymplectic effective General Boundary Field Theory | arXiv:1312.3220 | 2014 |
Vey D. | Multisymplectic geometry and the notion of observables | AIP Conf.Proc. 1446 (2012) 211-230 | 2012 |
Vey D. | n-plectic Maxwell Theory | arXiv:1303.2192 | 2013 |
Hélein F. | Multisymplectic formulation of Yang-Mills equations and Ehresmann connections | Advances in Theoretical and Mathematical Physics, Volume 19, Number 4, 805-835, 2015 arXiv:1406.3641 | 2015 |
Volterra V. | Sulle equazioni differenziali che provengono da questiono di calcolo delle variazioni | Rend. Cont. Acad. Lincei, ser. IV, vol. VI, (1890), 42-54. | 1890 |
Volterra V. | Sopra una estensione della teoria Jacobi-Hamilton del calcolo delle variazioni | Rend. Cont. Acad. Lincei, ser. IV, vol. VI, (1890),127-138. | 1890 |
Echeverria-Enriquez A., Munoz-Lecanda M.C., Roman-Roy N. | On the Multimomentum Bundles and the Legendre Maps in Field Theories | Rep. Math. Phys. 45(1) (2000) 85-105 arXiv:math-ph/9904007 | 2000 |
Echeverria-Enriquez A., Munoz-Lecanda M.C., Román-Roy N. | Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries | J. Phys. A 32(48) (1999) 8461-8484 arXiv:math-ph/9904007 | 1999 |
Echeverria-Enriquez A., Munoz-Lecanda M.C., Román-Roy N. | Reduction of Presymplectic Manifolds with Symmetry | Rev. Math. Phys. 11(10) (1999) 1209-1247 arXiv:math-ph/9911008 | 1999 |
Echeverria-Enriquez A., Munoz-Lecanda M.C., Román-Roy N. | Geometry of multisymplectic Hamiltonian first-order field theories | J.Math.Phys.41:7402-7444 (2000) arXiv:math-ph/0004005 | 2000 |
Echeverria-Enriquez A.,De Leon M., Munoz-Lecanda M.C., Román-Roy N. | Extended Hamiltonian systems in multisymplectic field theories | J. Math. Phys. 48(11) (2007) 112901 arXiv:math-ph/0506003 | 2007 |
De Leon M., Marin-Solano J., Marrero J.C., Munoz-Lecanda M.C., Roman-Roy N. | Pre-multisymplectic constraint algorithm for field theories | Int.J.Geom.Meth.Mod.Phys. 2 (2005) 839 arXiv:math-ph/0506005 | 2005 |
Roman-Roy N. | Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories | SIGMA 5 (2009), 100, 25 pages arXiv:math-ph/0506022 | 2009 |
Roman-Roy N., Salgado M., Vilarino S. | Higher-order Cartan symmetries in k-symplectic field theory | Int. J. Geom. Meth. Mod. Phys. 10(8) (2013) 1360013 (9 pp) arXiv:math-ph/0804.4785 | 2013 |
Ibort A., Spivak A. | Covariant Hamiltonian first order field theories with constraints on manifolds with boundary: the case of Hamiltonian dynamics | arXiv:math-ph/1511.03302 | 2015 |
Ibort A., Spivak A. | Covariant Hamiltonian Field Theories on Manifolds with Boundary: Yang-Mills Theories | arXiv:math-ph/1506.00338 | 2015 |
Khavkine I., | Covariant phase space, constraints, gauge and the Peierls formula | Int. J. Mod. Phys. A, 29, 1430009 (2014) arXiv:math-ph/1402.1282 | 2014 |
Khavkine I., | Presymplectic current and the inverse problem of the calculus of variations | arXiv:math-ph/1210.0802 | 2013 |