About Me

Profesor Titular
Applied Mathematics
Universidad Carlos III de Madrid (2009)

PhD - Theoretical Physics
Universidad Complutense de Madrid (2001)

Contact Details

Eduardo Jesús Sánchez Villaseñor
Universidad Carlos III de Madrid
Departamento de Matemáticas
Avda. de la Universidad 30

28911 Leganés - Spain
ejsanche@math.uc3m.es

Research

My research lies within the field of mathematical and theoretical physics. In particular I am interested in the study of classical and quantum aspects of general relativity, field theory, statistical mechanics and combinatorics.


List of publications [see also INSPIRE]

  1. Spacetime symmetries and geometric diffusion
    M Basquens, A Lasanta, E Mompó, V Varo, EJS Villaseñor
    Journal of Physics A: Mathematical and Theoretical 57 (2024) 285204
  2. Euclidean self-dual gravity: Ashtekar variables without gauge fixing
    F Barbero, M Basquens, EJS Villaseñor
    Physical Review D 109 (2024) 064047
  3. Dirac geometric approach for the unimodular Holst action
    B Díaz, EJS Villaseñor, D Zomeño
    Mathematics 12 (2024) 890
  4. Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra
    F Barbero, M Basquens, B Díaz, EJS Villaseñor
    Physica Scripta 97 (2022) 125202
  5. Edge observables of the Maxwell-Chern-Simons theory
    F Barbero, B Díaz, J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 106 (2022) 025011
  6. Consistent and non-consistent deformations of gravitational theories
    F Barbero, M Basquens, B Díaz, EJS Villaseñor
    Journal of High Energy Physics 05 (2022) 175
  7. Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
    J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 105 (2022) L101701
  8. On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries
    F Barbero, J Margalef-Bentabol, V Varo, EJS Villaseñor
    Physical Review D 105 (2022) 064066
  9. Covariant phase space for gravity with boundaries: metric versus tetrad formulations
    F Barbero, J Margalef-Bentabol, V Varo, EJS Villaseñor
    Physical Review D 104 (2021) 044048
  10. Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
    F Barbero, J Margalef-Bentabol, V Varo, EJS Villaseñor
    Physical Review D 104 (2021) 044046
  11. Three roads to the geometric constraint formulation of gravitational theories with boundaries
    F Barbero, M Basquens, V Varo, EJS Villaseñor
    Symmetry 13 (2021) 1430
  12. Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
    F Barbero, B Díaz, J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 103 (2021) 064062
  13. Concise symplectic formulation for tetrad gravity
    F Barbero, B Díaz, J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 103 (2021) 024051
  14. Geometric formulation of the covariant phase space methods with boundaries
    J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 103 (2021) 025011
  15. A two-sided Faulhaber-like formula involving Bernoulli polynomials
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Comptes Rendus Mathématique 357 (2020) 41
  16. On the asymptotics of the rescaled Appell polynomials
    F Barbero, J Salas, EJS Villaseñor
    Advances in Applied Mathematics 113 (2020) 101962
  17. Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary
    F Barbero, B Díaz, J Margalef-Bentabol, EJS Villaseñor
    Journal of High Energy Physics 1910 (2019) 121
  18. Dirac's algorithm in the presence of boundaries: a practical guide to a geometric approach
    F Barbero, B Díaz, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 36 (2019) 205014
  19. Adiabatic expansions for Dirac fields, renormalization, and anomalies
    F Barbero, A Ferreiro, J Navarro-Salas, EJS Villaseñor
    Physical Review D 98 (2018) 025016
  20. On the distribution of the eigenvalues of the area operator in loop quantum gravity
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 35 (2018) 065008
  21. Boundary Hilbert spaces and trace operators
    F Barbero, BA Juárez-Aubry, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 34 (2017) 095005
    CQG+ | Can boundaries and Hamiltonians get along?
  22. Functional evolution of scalar fields in bounded one-dimensional regions
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 34 (2017) 065004
  23. Hamiltonian dynamics of the parametrized electromagnetic field
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 33 (2016) 125030
  24. Hamiltonian description of the parametrized scalar field in bounded spatial regions
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 33 (2016) 105002
  25. Quantization of scalar fields coupled to point-masses
    F Barbero, BA Juárez-Aubry, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 32 (2015) 245009
  26. Generalized Stirling permutations and forests: higher-order Eulerian and Ward numbers
    F Barbero, J Salas, EJS Villaseñor
    Electronic Journal of Combinatorics 22(3) (2015) #P3.37
  27. Gauge invariance in simple mechanical systems
    F Barbero, J Prieto, EJS Villaseñor
    European Journal of Physics 36 (2015) 055005
  28. Bivariate generating functions for a class of linear recurrences: general structure
    F Barbero, J Salas, EJS Villaseñor
    Journal of Combinatorial Theory, Series A125 (2014) 146-165
  29. Topology of the Misner space and its g-boundary
    J Margalef-Bentabol, EJS Villaseñor
    General Relativity and Gravitation 46 (2014) 1755
  30. Separable Hilbert space for loop quantization
    F Barbero, T Pawłowski, EJS Villaseñor
    Physical Review D 90 (2014) 067505
  31. Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach
    F Barbero, J Prieto, EJS Villaseñor
    Classical and Quantum Gravity 31 (2014) 045021
    Selected by the Editorial Board of Classical and Quantum Gravity as one of the journal's Highlights of 2013-2014
  32. Band structure in the polymer quantization of the harmonic oscillator
    F Barbero, J Prieto, EJS Villaseñor
    Classical and Quantum Gravity 30 (2013) 165011
  33. Quantum isolated horizons and black hole entropy
    F Barbero, J Lewandowski, EJS Villaseñor
    PoS QGQGS2011 (2011) 023
  34. The thermodynamic limit and black hole entropy in the area ensemble
    F Barbero, EJS Villaseñor
    Classical and Quantum Gravity 28 (2011) 215014
  35. Statistical description of the black hole degeneracy spectrum
    F Barbero, EJS Villaseñor
    Physical Review D 83 (2011) 104013
  36. Detailed black hole state counting in loop quantum gravity
    I Agullo, F Barbero, EF Borja, J Diaz-Polo, EJS Villaseñor
    Physical Review D 82 (2010) 084029
  37. Quantization of midisuperspace models
    F Barbero, EJS Villaseñor
    Living Reviews in Relativity 13 (2010) 6
  38. Combinatorics of the SU(2) black hole entropy in loop quantum gravity
    I Agullo, F Barbero, EF Borja, J Diaz-Polo, EJS Villaseñor
    Physical Review D 80 (2009) 084006
  39. Flux-area operator and black hole entropy
    F Barbero, J Lewandowski, EJS Villaseñor
    Physical Review D 80 (2009) 044016
  40. The time-dependent quantum harmonic oscillator revisited: applications to quantum field theory
    D Gómez Vergel, EJS Villaseñor
    Annals of Physics 324 (2009) 1360-1385
  41. On the computation of black hole entropy in loop quantum gravity
    F Barbero, EJS Villaseñor
    Classical and Quantum Gravity 26 (2009) 035017
  42. Introduction to Quantum Mechanics
    EJS Villaseñor
    AIP Conference Proceedings 1023 (2008) 107
  43. Generating functions for black hole entropy in loop quantum gravity
    F Barbero, EJS Villaseñor
    Physical Review D 77 (2008) 121502(R)
  44. Quantum Einstein-Rosen waves: Coherent states and n-point functions
    F Barbero, I Garay, EJS Villaseñor
    Classical and Quantum Gravity 25 (2008) 205013
  45. Black hole state counting in loop quantum gravity: A number-theoretical approach
    I Agullo, F Barbero, EF Borja, J Diaz-Polo, EJS Villaseñor
    Physical Review Letters 100 (2008) 211301
  46. Unitary evolution of free massless fields in de Sitter space-time
    D Gómez Vergel, EJS Villaseñor
    Classical and Quantum Gravity 25 (2008) 145008
  47. Quantum unitary evolution of linearly polarized S1 x S2 and S3 Gowdy models coupled to massless scalar fields
    F Barbero, D Gómez Vergel, EJS Villaseñor
    Classical and Quantum Gravity 25 (2008) 085002
  48. Classical and quantum behavior of dynamical systems defined by functions of solvable Hamiltonians
    F Barbero, I Garay, EJS Villaseñor
    American Journal of Physics 76 (2008) 153
  49. Hamiltonian dynamics of linearly polarized Gowdy models coupled to massless scalar fields
    F Barbero, D Gómez Vergel, EJS Villaseñor
    Classical and Quantum Gravity 24 (2007) 5945
  50. Probing quantized Einstein-Rosen waves with massless scalar matter
    F Barbero, I Garay, EJS Villaseñor
    Physical Review D 74 (2006) 044004
  51. Evolution operators for linearly polarized two-Killing cosmological models
    F Barbero, D Gómez Vergel, EJS Villaseñor
    Physical Review D 74 (2006) 024003
  52. Exact quantization of Einstein-Rosen waves coupled to massless scalar matter
    F Barbero, I Garay, EJS Villaseñor
    Physical Review Letters 95 (2005) 051301
  53. Asymptotics of regulated field commutators for Einstein-Rosen waves
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Journal of Mathematical Physics 46 (2005) 062306
  54. Asymptotic analysis of field commutators for Einstein-Rosen gravitational waves
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Journal of Mathematical Physics 45 (2004) 3498
  55. Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Physical Review D 70 (2004) 044028
  56. Quantum cylindrical waves and sigma models
    F Barbero, GA Mena Marugán, EJS Villaseñor
    International Journal of Modern Physics D 13 (2004) 1119
  57. Time uncertainty in quantum gravitational systems
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Physical Review D 69 (2004) 044017
  58. Lorentz violations and euclidean signature metrics
    F Barbero, EJS Villaseñor
    Physical Review D 68 (2003) 087501
  59. Microcausality and quantum cylindrical gravitational waves
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Physical Review D 67 (2003) 124006
  60. Higher derivative fermionic field theories
    EJS Villaseñor
    Journal of Physics A: Mathematical and General 35 (2002) 6169
  61. Kinetic terms for 2-forms in four dimensions
    F Barbero, EJS Villaseñor
    Physical Review D 66 (2002) 045013
  62. Diff-invariant kinetic terms in arbitrary dimensions
    F Barbero, EJS Villaseñor
    Physical Review D 65 (2002) 125020
  63. Higher-derivative boson field theories as constrained second-order theories
    FJ de Urries, J Julve, EJS Villaseñor
    Journal of Physics A: Mathematical and General 34 (2001) 8919
  64. Quadratic s-form field actions with semi-bounded energy
    F Barbero, EJS Villaseñor
    Nuclear Physics B 600 (2001) 423
  65. BF actions for the Husain-Kuchař model
    F Barbero, EJS Villaseñor
    Physical Review D 63 (2001) 084021
  66. In search of local degrees of freedom in quadratic diff-invariant Lagrangians
    F Barbero, EJS Villaseñor
    Physical Review D 61 (2000) 104014
  67. Gauge fixing in higher derivative gravity
    A Bartoli, J Julve, EJS Villaseñor
    Classical and Quantum Gravity 16 (1999) 2283

Bachelor's degree courses


Calculus - Bachelor in Computer Science

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Program
Real numbers.
Sequences and series of real numbers.
Continuous functions.
Derivative.
Theorems about differentiable functions.
Taylor Expansions.
Applications of the Derivative.
Riemann integral
Fundamental theorem of Calculus.
Improper integrals.
Applications of Integration.

Course information - UC3M

Discrete Mathematics - Bachelor in Computer Science

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Program
Elementary set theory.
Graph theory.
Graph-theoretic algorithms.
Advanced techniques in combinatorics.
Equivalence relations.
Order relations.
Lattices.

Course information - UC3M


Master's degree courses


Perturbation Methods - Master in Industrial Mathematics

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Program
Basic notions of asymptotic analysis.
Approximation of integrals.
Solvability conditions for linear homogeneous problems.
Eigenvalue problems.
Poincare-Linstedt method.
Scaling of singular perturbation problems.
Boundary layer methods and matched asymptotic expansions.
Asymptotic expansions coupled method.
Method of multiple scales
Chapman-Enskog method.

Course information - M2i