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. 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
  2. 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
  3. Three roads to the geometric constraint formulation of gravitational theories with boundaries
    F Barbero, M Basquens, V Varo, EJS Villaseñor
    Symmetry 13 (2021) 1430
  4. 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
  5. Concise symplectic formulation for tetrad gravity
    F Barbero, B Díaz, J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 103 (2021) 024051
  6. Geometric formulation of the covariant phase space methods with boundaries
    J Margalef-Bentabol, EJS Villaseñor
    Physical Review D 103 (2021) 025011
  7. A two-sided Faulhaber-like formula involving Bernoulli polynomials
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Comptes Rendus Mathématique 357 (2020) 41
  8. On the asymptotics of the rescaled Appell polynomials
    F Barbero, J Salas, EJS Villaseñor
    Advances in Applied Mathematics 113 (2020) 101962
  9. 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
  10. 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
  11. Adiabatic expansions for Dirac fields, renormalization, and anomalies
    F Barbero, A Ferreiro, J Navarro-Salas, EJS Villaseñor
    Physical Review D 98 (2018) 025016
  12. 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
  13. 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?
  14. Functional evolution of scalar fields in bounded one-dimensional regions
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 34 (2017) 065004
  15. Hamiltonian dynamics of the parametrized electromagnetic field
    F Barbero, J Margalef-Bentabol, EJS Villaseñor
    Classical and Quantum Gravity 33 (2016) 125030
  16. 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
  17. 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
  18. 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
  19. Gauge invariance in simple mechanical systems
    F Barbero, J Prieto, EJS Villaseñor
    European Journal of Physics 36 (2015) 055005
  20. 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
  21. Topology of the Misner space and its g-boundary
    J Margalef-Bentabol, EJS Villaseñor
    General Relativity and Gravitation 46 (2014) 1755
  22. Separable Hilbert space for loop quantization
    F Barbero, T Pawłowski, EJS Villaseñor
    Physical Review D 90 (2014) 067505
  23. 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
  24. Band structure in the polymer quantization of the harmonic oscillator
    F Barbero, J Prieto, EJS Villaseñor
    Classical and Quantum Gravity 30 (2013) 165011
  25. Quantum isolated horizons and black hole entropy
    F Barbero, J Lewandowski, EJS Villaseñor
    PoS QGQGS2011 (2011) 023
  26. The thermodynamic limit and black hole entropy in the area ensemble
    F Barbero, EJS Villaseñor
    Classical and Quantum Gravity 28 (2011) 215014
  27. Statistical description of the black hole degeneracy spectrum
    F Barbero, EJS Villaseñor
    Physical Review D 83 (2011) 104013
  28. 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
  29. Quantization of midisuperspace models
    F Barbero, EJS Villaseñor
    Living Reviews in Relativity 13 (2010) 6
  30. 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
  31. Flux-area operator and black hole entropy
    F Barbero, J Lewandowski, EJS Villaseñor
    Physical Review D 80 (2009) 044016
  32. The time-dependent quantum harmonic oscillator revisited: applications to quantum field theory
    D Gómez Vergel, EJS Villaseñor
    Annals of Physics 324 (2009) 1360-1385
  33. On the computation of black hole entropy in loop quantum gravity
    F Barbero, EJS Villaseñor
    Classical and Quantum Gravity 26 (2009) 035017
  34. Introduction to Quantum Mechanics
    EJS Villaseñor
    AIP Conference Proceedings 1023 (2008) 107
  35. Generating functions for black hole entropy in loop quantum gravity
    F Barbero, EJS Villaseñor
    Physical Review D 77 (2008) 121502(R)
  36. Quantum Einstein-Rosen waves: Coherent states and n-point functions
    F Barbero, I Garay, EJS Villaseñor
    Classical and Quantum Gravity 25 (2008) 205013
  37. 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
  38. Unitary evolution of free massless fields in de Sitter space-time
    D Gómez Vergel, EJS Villaseñor
    Classical and Quantum Gravity 25 (2008) 145008
  39. 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
  40. 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
  41. 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
  42. Probing quantized Einstein-Rosen waves with massless scalar matter
    F Barbero, I Garay, EJS Villaseñor
    Physical Review D 74 (2006) 044004
  43. Evolution operators for linearly polarized two-Killing cosmological models
    F Barbero, D Gómez Vergel, EJS Villaseñor
    Physical Review D 74 (2006) 024003
  44. Exact quantization of Einstein-Rosen waves coupled to massless scalar matter
    F Barbero, I Garay, EJS Villaseñor
    Physical Review Letters 95 (2005) 051301
  45. Asymptotics of regulated field commutators for Einstein-Rosen waves
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Journal of Mathematical Physics 46 (2005) 062306
  46. Asymptotic analysis of field commutators for Einstein-Rosen gravitational waves
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Journal of Mathematical Physics 45 (2004) 3498
  47. Particles and vacuum for perturbative and non-perturbative Einstein-Rosen gravity
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Physical Review D 70 (2004) 044028
  48. Quantum cylindrical waves and sigma models
    F Barbero, GA Mena Marugán, EJS Villaseñor
    International Journal of Modern Physics D 13 (2004) 1119
  49. Time uncertainty in quantum gravitational systems
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Physical Review D 69 (2004) 044017
  50. Lorentz violations and euclidean signature metrics
    F Barbero, EJS Villaseñor
    Physical Review D 68 (2003) 087501
  51. Microcausality and quantum cylindrical gravitational waves
    F Barbero, GA Mena Marugán, EJS Villaseñor
    Physical Review D 67 (2003) 124006
  52. Higher derivative fermionic field theories
    EJS Villaseñor
    Journal of Physics A: Mathematical and General 35 (2002) 6169
  53. Kinetic terms for 2-forms in four dimensions
    F Barbero, EJS Villaseñor
    Physical Review D 66 (2002) 045013
  54. Diff-invariant kinetic terms in arbitrary dimensions
    F Barbero, EJS Villaseñor
    Physical Review D 65 (2002) 125020
  55. 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
  56. Quadratic s-form field actions with semi-bounded energy
    F Barbero, EJS Villaseñor
    Nuclear Physics B 600 (2001) 423
  57. BF actions for the Husain-Kuchař model
    F Barbero, EJS Villaseñor
    Physical Review D 63 (2001) 084021
  58. In search of local degrees of freedom in quadratic diff-invariant Lagrangians
    F Barbero, EJS Villaseñor
    Physical Review D 61 (2000) 104014
  59. 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