Research publications

• J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
  "Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems"
  Int. J. Geometric Methods in Mod. Phys. 7 (2010) to appear
  arXiv: 0908.2453 abstract
• X. Gràcia, R. Martín and N. Román-Roy
  "Constraint algorithm for k-presymplectic hamiltonian systems. Application to singular field theories"
  Int. J. Geometric Methods in Mod. Phys. 6 (2009) 851-872
  journal    arXiv: 0903.1791 abstract
• J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
  "Hamilton-Jacobi theory and the evolution operator", pp. 177-186 in
  Mathematical physics and field theory. Julio Abad, in memoriam
  edited by M. Asorey, J.V. García Esteve, M.F. Rañada and J. Sesma
  (Prensas Universitarias de Zaragoza, 2009)   ISBN: 978-84-92774-04-3
  pdf    arXiv:0907.1039 abstract
• X. Gràcia and R. Martín
  "Vector hulls of affine spaces and affine bundles"
  Acta Applicandae Mathematicae 103 (2008) 101-129
  journal    abstract
• J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
  "A new geometrical setting for the Hamilton-Jacobi equation", pp. 198-204 in
  Proceedings of the XIV Fall Workshop on Geometry and Physics, Bilbao, 2005
  Publicaciones de la RSME, 10
  (Real Sociedad Matemática Española, Madrid, 2006)   ISBN: 84-933610-7-0
• J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.-C. Muñoz-Lecanda and N. Román-Roy
  "Geometric Hamilton-Jacobi theory"
  Int. J. Geometric Methods in Mod. Phys. 3 (2006) 1417-1458
  journal    arXiv: math-ph/0604063 abstract
• X. Gràcia and R. Martín
  "Vector hulls and jet bundles", pp. 215-220 in
  Proceedings of the XIII Fall Workshop on Geometry and Physics, Murcia, 2004
  Publicaciones de la RSME, 9
  (Real Sociedad Matemática Española, Madrid, 2005)   ISBN: 84-933610-6-2
• X. Gràcia and R. Martín
  "Geometric aspects of time-dependent singular differential equations"
  Int. J. Geometric Methods in Mod. Phys. 2 (2005) 597-618
  journal    abstract    arXiv: math-ph/0410051 abstract
• X. Gràcia and R. Martín
  "Regularity and symmetries of nonholonomic systems"
  J. Phys. A: Math. Gen. 38 (2005) 1071-1087
  journal    abstract    arXiv: math-ph/0405066 abstract
• X. Gràcia and R. Martín
  "Time-dependent singular systems", pp. 155-160 in
  Proceedings of the XII Fall Workshop on Geometry and Physics, Coimbra, 2003
  edited by H. Albuquerque, R. Caseiro, J. Clemente-Gallardo, J.M. Nunes da Costa and J. Teles.
  Publicaciones de la RSME, 7
  (Real Sociedad Matemática Española, Madrid, 2004)   ISBN: 84-933610-3-8
  
• X. Gràcia, M.-C. Muñoz-Lecanda and N. Román-Roy
  "On some aspects of the geometry of differential equations in physics"
  Int. J. Geometric Methods in Mod. Phys. 1 (2004) 265-284
  journal    abstract    arXiv: math-ph/0402030 abstract
• X. Gràcia and R. Martín
  "Nonholonomic systems and the relativistic particle", pp. 223-228 in
  Proceedings of the XI Fall Workshop on Geometry and Physics, Oviedo, 2002
  edited by J. Fernández Núñez, W. García Fuertes and A. Viña Escalar
  Publicaciones de la RSME, 6
  (Real Sociedad Matemática Española, Madrid, 2004)   ISBN: 84-933610-1-1
  
• X. Gràcia and J.M. Pons
  "Symmetries of singular differential equations", pp. 159-168 in
  Proceedings of the X Fall Workshop on Geometry and Physics, Miraflores de la Sierra, 2001
  edited by A. González-López, M. Mañas, L. Martínez Alonso and M.Á. Rodríguez
  Publicaciones de la RSME, 4
  (Real Sociedad Matemática Española, Madrid, 2003)   ISBN: 84-923818-8-4
  
• X. Gràcia, J. Marín-Solano and M.-C. Muñoz-Lecanda
  "Some geometric aspects of variational calculus in constrained systems"
  Rep. Math. Phys. 51 (2003) 127-148
  journal    abstract    arXiv: math-ph/0004019 abstract
• X. Gràcia and J.M. Pons
  "Symmetries and infinitesimal symmetries of singular differential equations"
  J. Phys. A: Math. Gen. 35 (2002) 5059-5077
  journal    abstract    arXiv: math-ph/0201034 abstract
• X. Gràcia and J.M. Pons
  "Some new geometric structures for singular lagrangians", pp. 227-232 in
  Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltrú, 2000
  edited by X. Gràcia, J. Marín-Solano, M.-C. Muñoz-Lecanda and N. Román-Roy
  Publicaciones de la RSME, 3
  (Real Sociedad Matemática Española, Madrid, 2001)   ISBN: 84-923818-5-X
  abstract    compressed PS (62 KB).
• X. Gràcia and J.M. Pons
  "Singular lagrangians: some geometric structures along the Legendre map"
  J. Phys. A: Math. Gen. 34 (2001) 3047-3070
  journal    abstract    arXiv: math-ph/0009038 abstract
• X. Gràcia and J.M. Pons
  "Canonical Noether symmetries and commutativity properties for gauge systems"
  J. Math. Phys. 41 (2000) 7333-7351
  abstract    arXiv: math-ph/0007037 abstract
• X. Gràcia, J. Marín-Solano and M.-C. Muñoz-Lecanda
  "Variational principles in mechanics: geometric aspects", pp. 81-94 in
  Séptimo encuentro de otoño de geometría diferencial y sus aplicaciones
  edited by E. Llinares and J. Monterde
  Publicaciones de la RSME, 1
  (Real Sociedad Matemática Española, Madrid, 2000)   ISBN: 84-923818-1-7
  abstract,    compressed PS (1345 KB) extracted from the proceedings
• X. Gràcia
  "Fibre derivatives: some applications to singular lagrangians"
  Rep. Math. Phys. 45 (2000) 67-84
  abstract    arXiv: math-ph/0007038 abstract
• X. Gràcia
  "The fibre derivative and some of its applications"
  Proceedings of the V Fall Workshop: Geometry and Physics, 1996
  edited by J.F. Cariñena, E. Martínez and M.F. Rañada.
  Mem. Real Acad. Cienc. Exact. Fís. Nat. Madrid 32 (1998) 43-58
  abstract
• X. Gràcia and J.M. Pons
  "Noether (and gauge) transformations for higher order singular lagrangians"
  Proceedings of the Third Meeting on Current Ideas in Mechanics and Related Fields, Segovia (Spain), June 19-23, 1995
  Extracta Mathematicae 11 (1996) 65-79
  abstract
• X. Gràcia, M.C. Muñoz-Lecanda and N. Román-Roy
  "Singular systems: their origins, general features, and non numerical solution", pp. 31-36 in
  System Structure and Control 1995.   A Proceedings volume from the IFAC Conference, Nantes, France, 5-7 July 1995
  edited by M. Guglielmi, Laboratoire d'Automatique de Nantes
  (Elsevier, 1996)   ISBN: 0-08-042356-6
  abstract
• X. Gràcia and J.M. Pons
  "Gauge transformations for higher-order lagrangians"
  J. Phys. A: Math. Gen. 28 (1995) 7181-7196
  abstract    arXiv: hep-th/9509094 abstract
• X. Gràcia and J.M. Pons
  "Noether transformations with vanishing conserved quantity"
  Ann. Inst. H. Poicaré A 61 (1994) 315-327
  abstract
• X. Gràcia, J.M. Pons and J. Roca
  "Finite gauge transformations: the reparametrization algebras", pp. 21-27 in
  Proceedings of the Fall Workshop on Differential Geometry and its Applications, Barcelona '93
  edited by X. Gràcia, M.C. Muñoz and N. Román, 1994
  ISBN 84-605-1284-3
  abstract
• X. Gràcia, J.M. Pons and J. Roca
  "Closure of reparametrization algebras and flow-dependence of finite reparametrizations"
  Int. J. Mod. Phys. A 9 (1994) 5001-5017
  abstract
• X. Gràcia and J. Roca
  "Covariant and noncovariant gauge transformations for the conformal particle"
  Mod. Phys. Lett. A 8 (1993) 1747-1761
  abstract
• X. Gràcia and J.M. Pons
  "A hamiltonian approach to lagrangian Noether transformations"
  J. Phys. A: Math. Gen. 25 (1992) 6357-6369
  abstract
• X. Gràcia and J.M. Pons
  "A generalized geometric framework for constrained systems"
  Diff. Geom. Appl. 2 (1992) 223-247
  journal    abstract
• X. Gràcia, J.M. Pons and N. Román-Roy
  "Higher order conditions for singular lagrangian dynamics"
  J. Phys. A: Math. Gen. 25 (1992) 1989-2004
  abstract
• X. Gràcia
  Sistemes lligats: estudi geomètric i transformacions de simetria (in Catalan)
  [Constrained systems: geometric study and symmetry transformations]
  Ph. D. thesis, University of Barcelona, 1991.
  Advisor: Josep M. Pons
  ISBN 84-7875-790-2
  abstract (English)
• X. Gràcia, J.M. Pons and N. Román-Roy
  "Higher order lagrangian systems: geometric structures, dynamics, and constraints"
  J. Math. Phys. 32 (1991) 2744-2763
  abstract
• X. Gràcia and J.M. Pons
  "Constrained systems: a unified geometric approach"
  Int. J. Theor. Phys. 30 (1991) 511-516
  abstract
• C. Batlle, J. Gomis, X. Gràcia and J.M. Pons
  "Noether's theorem and gauge transformations: application to the bosonic string and CP₂^n-1 model"
  J. Math. Phys. 30 (1989) 1345-1350
  abstract
• X. Gràcia and J.M. Pons
  "On an evolution operator connecting lagrangian and hamiltonian formalisms"
  Lett. Math. Phys. 17 (1989) 175-180
  abstract
• X. Gràcia and J.M. Pons
  "Gauge generators, Dirac's conjecture, and degrees of freedom for constrained systems"
  Ann. Phys. (N.Y.) 187 (1988) 355-368
  journal    abstract
• X. Gràcia
  Transformacions de gauge en sistemes dinàmics de dimensió finita (in Catalan)
  [Gauge transformations in dynamical systems of finite dimension]
  Degree thesis, University of Barcelona, 1987.
  Advisor: Josep M. Pons
  contents (English translation)

• X. Gràcia, J. Marín-Solano, M.-C. Muñoz-Lecanda and N. Román-Roy (editors) Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltrú, 2000 Publicaciones de la RSME, vol. 3 Real Sociedad Matemática Española, Madrid, 2001 xii+270 pages      ISBN: 84-923818-5-X available also from the editors Electronic version

• X. Gràcia, M.C. Muñoz and N. Román (editors) Proceedings of the Fall Workshop on Differential Geometry and its Applications, Barcelona '93 published in Barcelona by the editors, 1994 x+80 pages      ISBN 84-605-1284-3 contents, preface available from the editors

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Last update: 30 December 2009