sample of publications

• articles 

  • Groupoid and algebra of the infinite quantum spin chain.  JOURNAL OF GEOMETRY AND PHYSICS.  191:1-23. 2023
  • The sky invariant: A new conformal invariant for Schwarzschild spacetime.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  19:2250168-1-2250168-27. 2022
  • Correction: The space of light rays: causality and L-boundary (General Relativity and Gravitation, (2022), 54, 6, (59)).  GENERAL RELATIVITY AND GRAVITATION.  54:1-2. 2022
  • Quantum tomography and Schwinger's picture of quantum mechanics.  Journal of Physics A-Mathematical and Theoretical.  55:1-23. 2022
  • The space of light rays: Causality and L-boundary.  GENERAL RELATIVITY AND GRAVITATION.  54:1-64. 2022
  • Causality in Schwinger's Picture of Quantum Mechanics.  Entropy (Entropy).  24:75-92. 2022
  • Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds.  Symmetry.  14:1-28. 2022
  • Dynamical maps and Symmetroids.  OPEN SYSTEMS & INFORMATION DYNAMICS.  28:2150019. 2021
  • Schwinger's picture of quantum mechanics: 2-groupoids and symmetries.  Journal of Geometric Mechanics.  13:333-354. 2021
  • Feynman's propagator in Schwinger's picture of Quantum Mechanics.  MODERN PHYSICS LETTERS A.  36:1-17. 2021
  • A quantum route to the classical Lagrangian formalism.  MODERN PHYSICS LETTERS A.  36. 2021
  • Representation of non-semibounded quadratic forms and orthogonal additivity.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  495:1-25. 2021
  • Quantum tomography and the quantum Radon transform.  Inverse Problems and Imaging.  15:893-928. 2021
  • Evolution of classical and quantum states in the groupoid picture of quantum mechanics.  Entropy (Entropy).  22:1-18. 2020
  • Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein&-Gordon and Schrödinger.  MODERN PHYSICS LETTERS A.  35. 2020
  • Covariant variational evolution and Jacobi brackets: Fields.  MODERN PHYSICS LETTERS A.  35. 2020
  • Covariant variational evolution and Jacobi brackets: Particles.  MODERN PHYSICS LETTERS A.  35. 2020
  • Lagrangian description of Heisenberg and Landau-von Neumann equations of motion.  MODERN PHYSICS LETTERS A.  35. 2020
  • Schwinger's picture of quantum mechanics.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  17. 2020
  • Schwinger's picture of quantum mechanics IV: Composition and independence.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  17. 2020
  • Groupoids and Coherent States.  OPEN SYSTEMS & INFORMATION DYNAMICS.  26. 2020
  • Remembering George Sudarshan.  Quantum Reports.  1:271-276. 2019
  • Knit Product of Finite Groups and Sampling.  Mediterranean Journal of Mathematics.  16:1-16. 2019
  • Manifolds of classical probability distributions and quantum density operators in infinite dimensions.  INFORMATION GEOMETRY.  2:231-271. 2019
  • Descriptions of Relativistic Dynamics with World Line Condition.  Quantum Reports.  1:181-192. 2019
  • Schwinger's picture of quantum mechanics III: The statistical interpretation.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  16. 2019
  • Schwinger's picture of quantum mechanics I: Groupoids.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  16:1-31. 2019
  • Schwinger's picture of quantum mechanics II: Algebras and observables.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  16. 2019
  • On the Structure of Finite Groupoids and Their Representations.  Symmetry.  11:1-28. 2019
  • Nilpotent integrability, reduction of dynamical systems and a third-order Calogero-Moser system.  ANNALI DI MATEMATICA PURA ED APPLICATA.  198:1513-1540. 2019
  • Stratified manifold of quantum states, actions of the complex special linear group.  Annals of Physics.  400:221-245. 2019
  • L-extensions and L-boundary of conformal spacetimes.  GENERAL RELATIVITY AND GRAVITATION.  50 :1-47. 2018
  • A gentle introduction to Schwinger's formulation of quantum mechanics: The groupoid picture.  MODERN PHYSICS LETTERS A.  33:112-122. 2018
  • Solving quantum optimal control problems using Clebsch variables and Lin constraints.  Journal of Physics A-Mathematical and Theoretical.  51. 2017
  • Geometrical structures for classical and quantum probability spaces.  INTERNATIONAL JOURNAL OF QUANTUM INFORMATION.  15. 2017
  • A new algorithm for computing branching rules and Clebsch-Gordan coefficients of unitary representations of compact groups.  JOURNAL OF MATHEMATICAL PHYSICS.  58:1-23. 2017
  • Dynamical aspects in the quantizer-dequantizer formalism.  Annals of Physics.  385:769-781. 2017
  • Dynamical vector fields on the manifold of quantum states.  OPEN SYSTEMS & INFORMATION DYNAMICS.  24. 2017
  • Admissible boundary conditions for Hamiltonian field theories.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  14 (1740006). 2017
  • Covariant Jacobi brackets for test particles.  MODERN PHYSICS LETTERS A.  32. 2017
  • Covariant brackets for particles and fields.  MODERN PHYSICS LETTERS A.  32:1-16. 2017
  • Covariant Hamiltonian field theories on manifolds with boundary: Yang-Mills theories.  Journal of Geometric Mechanics.  9:47-82. 2017
  • A conformal boundary for space-times based on light-like geodesics: the 3-dimensional case.  JOURNAL OF MATHEMATICAL PHYSICS.  58. 2017
  • Covariant Hamiltonian first-order field theories with constraints, on manifolds with boundary: the case of Hamiltonian dynamics.  Banach Center Publications.  110:87-104. 2016
  • Modeling Sampling in Tensor Products of Unitary Invariant Subspaces.  Journal of Function Spaces.  2016
  • The quantum-to-classical transition: contraction of associative products.  PHYSICA SCRIPTA.  91. 2016
  • Optimal control of two coupled spinning particles in the Euler-Lagrange picture.  Journal of Physics A-Mathematical and Theoretical.  49. 2016
  • On self-adjoint extensions and symmetries in quantum mechanics.  ANNALES HENRI POINCARE.  16:2367-2397. 2015
  • Boundary dynamics and topology change in quantum mechanics.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  12. 2015
  • On the theory of self-adjoint extensions of symmetric operators and its applications to quantum physics.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  12. 2015
  • Quantum Tomography twenty years later.  PHYSICA SCRIPTA.  90. 2015
  • The topology and geometry of self-adjoint and elliptic boundary conditions for Dirac and Laplace operators.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  12. 2015
  • Causality and skies: is non-refocussing necessary?.  CLASSICAL AND QUANTUM GRAVITY.  32. 2015
  • Self-adjoint extensions of the Laplace-Beltrami operator and unitaries at the boundary.  JOURNAL OF FUNCTIONAL ANALYSIS.  268:634-670. 2015
  • Boundary dynamics driven entanglement.  Journal of Physics A-Mathematical and Theoretical.  47. 2014
  • Boundary dynamics driven entanglement: Quantum control in its many facets is a key notion in quantum information technologies.  Europhysics News (Europhysics News).  45:18. 2014
  • On the space of light rays of a spacetime and a reconstruction theorem by Low.  CLASSICAL AND QUANTUM GRAVITY.  31. 2014
  • On the multilinear Hausdorff problem of moments.  Revista Matematica Complutense.  27:213-224. 2014
  • Groupoids and the tomographic picture of quantum mechanics.  PHYSICA SCRIPTA.  88:1-12. 2013
  • Convex bodies of states and maps.  Journal of Physics A-Mathematical and Theoretical.  46. 2013
  • Null phase curves and manifolds in geometric phase theory.  JOURNAL OF MATHEMATICAL PHYSICS.  54. 2013
  • Reduction of Lie-Jordan algebras: Classical.  Nuovo Cimento della Societa Italiana di Fisica C (Nuovo Cimento della Societa Italiana di Fisica C).  36C:107-115. 2013
  • Reduction of Lie-Jordan algebras: Quantum.  Nuovo Cimento della Societa Italiana di Fisica C (Nuovo Cimento della Societa Italiana di Fisica C).  36C:117-125. 2013
  • Realization of associative products in terms of Moyal and tomographic symbols.  PHYSICA SCRIPTA.  87:1-6. 2013
  • Numerical Solutions of the Spectral Problem for Arbitrary Self-Adjoint Extensions of the One-Dimensional Schrödinger Equation.  SIAM JOURNAL ON NUMERICAL ANALYSIS.  51:1254-1279. 2013
  • Reduction of Lie-Jordan Banach algebras and quantum states.  Journal of Physics A-Mathematical and Theoretical.  46:1-14. 2013
  • Invariant forms and automorphisms of locally homogeneous multisymplectic manifolds.  Journal of Geometric Mechanics.  4:397-419. 2012
  • The geometry of integrable and superintegrable systems.  THEORETICAL AND MATHEMATICAL PHYSICS.  172:1109-1117. 2012
  • On the tomographic description of classical fields.  PHYSICS LETTERS A.  376:1417-1425. 2012
  • Folding and unfolding quantum states.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  9:1-13. 2012
  • A representation theorem for orthogonally additive polynomials in Riesz Spaces.  Revista Matematica Complutense.  25:21-30. 2012
  • A pedagogical presentation of a C*-algebraic approach to quantum tomography.  PHYSICA SCRIPTA.  84:1-19. 2011
  • Quantum geons on noncommutative spacetimes.  GENERAL RELATIVITY AND GRAVITATION.  43:3531-3567. 2011
  • Optimal control realizations of Lagrangian systems with symmetry.  INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS.  8:1627-1651. 2011
  • Covariant quantum fields on noncommutative spacetimes.  JOURNAL OF HIGH ENERGY PHYSICS.  2011:1-17. 2011
  • Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology.  Symmetry Integrability and Geometry-Methods and Applications.  6:52-77. 2010
  • Inequivalence of Quantum Field Theories on Noncommutative Spacetimes: Moyal versus Wick-Voros Planes.  PHYSICAL REVIEW D.  81. 2010
  • On the Tomographic Picture of Quantum Mechanics.  PHYSICS LETTERS A.  374:2614-2617. 2010
  • On the Multilinear Trigonometric Problem of Moments.  Contemporary Mathematics (Contemporary Mathematics).  507:141-153. 2010
  • A Numerical Algorithm for Singular Optimal LQ Control Systems.  NUMERICAL ALGORITHMS.  51:477-500. 2009
  • Remarks on the Star Product of Functions on Finite and Compact Groups.  PHYSICS LETTERS A.  373:401-408. 2009
  • An Introduction to the Tomographic Picture of Quantum Mechanics.  PHYSICA SCRIPTA.  79. 2009
  • On the Representation of Orthogonally Additive Polynomials in lp.  PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES.  45:519-524. 2009
  • Geometrical Description of Aglebraic Structures: Applications to Quantum Mechanics.  AIP Conference Proceedings (AIP Conference Proceedings).  1130:47-59. 2009
  • A Generalized Wigner Function on the Space of Irreducible Representations of the Weyl-Heisenberg Group and its Transformation Properties.  Journal of Physics A-Mathematical and Theoretical.  42:155302-155313. 2009
  • Quantum Control and Representation Theory.  Journal of Physics A-Mathematical and Theoretical.  42. 2009

• book chapters 

  • Towards a Quantum Sampling Theory: The Case of Finite Groups. In: Classical and Quantum Physics: 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control.  SPRINGER. 203-229. 2019
  • On the Notion of Composite System. In: Geometric Science of Information: 4th International Conference, GSI 2019, Toulouse, France, August 27-29, 2019: Proceedings.  SPRINGER. 647-654. 2019
  • Differential Geometry of Quantum States, Observables and Evolution. In: Quantum Physics and Geometry.  SPRINGER. 153-172. 2019
  • The contact structure in the space of light rays. In: A Mathematical Tribute to Professor José María Montesinos Amilibia.  EDITORIAL COMPLUTENSE, S.A.. 133-159. 2015
  • Clebsch Variables, Lin Constraints and Quantum Control. In: Mathematical Physics and Field Theory: Julio Abad, "in memorim".  Editorial Prensas Universitarias de Zaragoza. 255-266. 2009

• books 

  • An Introduction to Groups, Groupoids and Their Representations.  CRC PRESS. 2019
  • Geometry from Dynamics, Classical and Quantum.  SPRINGER. 2015

• conference contributions 

  • On the foundations of the multisymplectic description of eld theories.  2-2. 2020
  • On the notion of composite system.  647-654. 2019
  • Groupoids and frames: a new setting for sampling 2018
  • Groupoids, categories and Quantum Mechanics 2018
  • Quantum control on the boundary 2018
  • The geometry of the l-boundary and conformal extensions 2018
  • Variational Principles in Quantum Physics 2018
  • 
    Geometry and spaces of classical probability states 2017
  • Covariant Brackets in Field Theories and Particle Dynamics 2017
  • Sesión Especial: Avances recientes en Geometría, Mecánica y Control 2017
  • The covariant Hamiltonian formalism of field theories on manifolds with boundaries 2017
  • V International Workshop on Mathematical Foundations of Quantum Mechanics and its applications. 2017
  • On a class of integrable Hamiltonian systems related to the optimal control problem of two coupled spins 2016
  • On the steps of Shannon's sampling theorem: towards a theory of quantum sampling 2016
  • Causality and the contact structure on the space of light rays 2015
  • On the Atiyah's index Theorem for manifolds with boundary and the eta-invariant. 2015
  • On the multisymplectic formalism of first-order Hamiltonian field theories on manifolds with boundary: an application to Palatini's gravity 2015
  • Convex bodies of states, majorization and Atiyah's convexity theorem 2014
  • Mentes y máquinas: Ciencia-ficción, Física y Matemáticas 2014
  • On Kato's representation theorem for a class of functions on infinite dimensional Kähler manifolds 2014
  • On a Class of Kählerian Hamiltonian Systems on Infinite Dimensional Kähler Manifolds with Holomorphic Flows 2014
  • On the geometrical foundations of Field Theories on manifolds with boundary: Palatinis formulation of gravity 2014
  • On the structure of Schwinger's measurement algebra: groups, groupoids and 2-groupoids 2014
  • Operadores no acotados en Espacios de Hilbert(Tema A.1) 2014
  • First order Hamiltonian field theories in manifolds with boundary: the Nambu sigma model 2013
  • On a symplectic Radon transform 2013
  • On the notion of integrability of dynamical systems: nilpotent integrability and serendipity 2013
  • Quantum holonomy control and quantum control at the boundary 2013
  • Quantum walks and dynamics on graphs 2013
  • Reduction of Jordan and Lie-Jordan Banach algebra 2013
  • The Poisson sigma model revisited 2013
  • There is plenty of room at the boundary 2013
  • Three lectures on global boundary conditions and the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on Riemannian manifolds with boundary.  15-54. 2012
  • Reduction of Optimal Control Problems with Symmetry and Dirac Structures 2011
  • Road to tomography of fields 2011