LIBRARY: Multisymplectic Geometry & Field Theory

 

Author(s) Title References Year
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