Search

14 pags., We analyze the Lagrangian and Hamiltonian formulations of the Maxwell-Chern-Simons theory defined on a manifold with boundary for two different sets of boundary equations derived from a variational principle. We pay special attention to the identification of the infinite chains of boundary constraints and their resolution. We identify edge observables and their algebra [which corresponds to the well-known U(1) Kac-Moody algebra]. Without performing any gauge fixing, and using the Hodge-Morrey theorem, we solve the Hamilton equations whenever possible. In order to give explicit solutions, we consider the particular case in which the fields are defined on a 2-disk. Finally, we study the Fock quantization of the system and discuss the quantum edge observables and states., This work has been supported by the Spanish Ministerio de Ciencia Innovación y Universidades-Agencia Estatal de Investigación PID2020–116567GB-C22 grant. B. D. acknowledges support from the CONEX-Plus program funded by Universidad Carlos III de Madrid and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 801538. J. M.-B. is supported by the AARMS postdoctoral fellowship, by the NSERC Discovery Grant No. 2018-04873, and the NSERC Grant No. RGPIN-2018-04887. E. J. S. V. is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).

4 pags., We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in particular, a Faulhaber-like formula for sums of the form 1(n−1) +2(n−2) +···+(n−1)1 for positive integers m and n., This work has been supported by the Spanish Ministerio de Ciencia Innovación y Universidades Agencia Estatal de Investigación/ FIS2017-84440-C2-2-P grant. Juan Margalef-Bentabol is supported by 2017SGR932 AGAUR/Generalitat de Catalunya, MTM2015-69135-P/FEDER, MTM2015-65715-P, and the ERC Starting Grant with number 335079. He is also supported in part by the Eberly Research Funds of Penn State, by the NSF grant PHY-1806356, and by the Urania Stott fund of Pittsburgh foundation UN2017-92945.

Conference on the occasion of Jerzy Lewandowski's 60th birthday (Jurekfest). -- Presentación de 38 diapositivas, University of Warsaw, Warszawa, Poland, September 16-20, 2019, Constrained systems play a central role in quantum field theory, in particular in those frameworks relying on canonical quantization such as Loop Quantum Gravity. The method of choice for the Hamiltonian treatment of singular Lagrangian systems relies on the celebrated Dirac algorithm. In the present talk we review this approach from a geometric perspective in a way that it is tailored to the treatment of field theories. We will pay special attention to a number of issues that play an special role in the presence of spatial boundaries.

In this paper we study a family of generalizations of the Pontryagin and Husain-Kucha�� actions on manifolds with boundary. In some cases, they describe well-known models---either at the boundary or in the bulk---such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kucha�� model. We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here. This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors., 15 pages

Boundaries, GNH, and parametrized theories. It takes three to tango. This is the motto of my doctoral thesis and the common thread of it. The thesis is structured as follows: after some acknowledgments and a brief introduction, chapter one is devoted to establishing the mathematical background necessary for the rest of the thesis (with special emphasis in the space of embeddings and the Fock construction). Chapter two is based on our papers arXiv:1701.00735, arXiv:1611.09603, and arXiv:1501.05114. We study carefully a system consisting of a string with two masses attached to the ends and try to establish if we can identify degrees of freedom at the boundary both classically and quantically (spoiler alert: it is not possible). The next chapter is a brief introduction to the parametrized theories with the simple example of the parametrized classical mechanics. The 4th chapter deals with the parametrized electromagnetism with boundaries, a generalization of our paper arXiv:1511.00826. The following chapter focuses on the parametrized scalar field with boundaries (see arXiv:1507.05438). The 6th chapter deals with the parametrized Maxwell-Chern-Simons and Chern-Simons theories with boundaries. Chapter seven delves into the theory of general relativity using the GNH algorithm, showing that the Hamiltonian formulation (ADM) can be obtained in a more direct and simple way. The same study is performed over the unimodular gravity. In the last chapter we gather the conclusions and some hints about the future work. Finally, an appendix is included with some additional mathematical topics as well as explicit computations., Ph.D. thesis in mathematical physics. 182 pages. New versions to correct minor typos and add/update references

Mención Internacional en el título de doctor Programa Oficial de Doctorado en Ingeniería Matemática Presidente: José Navarro Salas.- Secretario: Jesús Salas Martínez.- Vocal: Iván Agulló Rodenas

Fifteenth Marcel Grossmann Meeting - July 1-7 .MG15.University of Rome "La Sapienza" - Rome, Italy (2018). -.http://www.icra.it/mg/mg15/

València (Spain) on Nov. 29-30th and Dec. 1st. (2017). -- https://www.uv.es/blackholes/PGTh_2017/home.html, Many apparent space-time pathological behaviours are due to a lack of understanding of the geometry. On the other hand, intrinsic pathologies are the trademark of singular space-times. In this talk I will show how topology helps us understanding both situtations in the so called Misner space.

Presentación de 55 diapositivas. -- Centro Nacional de Física de Partículas, Astropartículas y Nuclear, Santander, 23-25 octubre 2017. -- https://indico.ific.uv.es/event/2960/

CEDYA + CMA 2017, Cartagena, 26 al 30 de Junio de 2017

Tenerife, Canary Islands, Spain, January 16-20, 2017. -- http://5ibamgmc.webs.ull.es/, In this talk I will discuss a simple system consisting of a 1D field coupled to point-masses. Despite its simplicity, it is necessary to introduce appropriate functional spaces defined with non standard measures and use appropriate geometric methods to deal with it. Some interesting questions arise at both classical and quantum levels. We will show, in particular, that the quantum Fock space cannot be written in a natural way as a tensor product of Hilbert spaces associated with the field and the point masses respectively. This is somehow unexpected and poses some questions regarding the physical interpretation of the system.

Non Linear Integrable Systems; Burgos (Spain); october 20-22, 2016; https://integrabilityworkshop.wordpress.com/about/

Presentación 43 diapositivas; 21st International Conference on General Relativity and Gravitation; New York (USA); 11-15 July 2016; http://www.gr21.org/program.html, Parametrized field theories provide interesting examples of relatively simple diff- invariant systems, which can be then used as good toy models to understand some subtle features of General Relativity. In this talk, relying on the space of embeddings, I will explain some interesting aspects of the parametrized electromagnetic field, as it is one of the simplest models with gauge symmetries. In particular I will focus on how its primary constraint submanifold can be divided into sectors where different Hamiltonian dynamics take place, and show how the Gauss law comes into play (spoiler alert, it is not a constraint)

10th International young researcher workshop on GMC (Mechanics, Geometry and Control); Institut Henri Poincaré, Paris, France. January 13-15, 2016; http://gmcnet.webs.ull.es/?q=activity-detaill/1396

Presentación de 115 diapositivas; 24 IFW Geometry and Physics, Centro Universitario de la Defensa of Zaragoza (Spain) on September 1-4 2015; http://cud.unizar.es/xxivifwgpzgz/home

In this paper, using the notions of perturbation and contraction of Lie and Leibniz algebras, we show that the algebraic varieties of Leibniz and nilpotent Leibniz algebras of dimension greater than 2 are reducible., Comment: 7 pages, translation from the original french published version (2007). Second version: corrected typos

2nd i-Link Workshop Macro from Micro, celebrado en Madrid de 15 al 17 de septiembre de 2014.

Boundaries are relevant in quantum field theory (QFT) and play a fundamental role in gravity, in particular regarding the physics of black holes and cosmology. The presence or absence of boundary degrees of freedom is especially important. We discuss here a simple linear model where classical boundary degrees of freedom are introduced from the start and study --by precisely constructing the Hamiltonian formulation and the Fock space quantization-- the relevant Hilbert spaces and important observables in the presence of boundaries. We will briefly discuss the physical implications of our model, both from the point of view of quantum mechanics and QFT.

This thesis investigates the metric and tetrad formulations of three gravitational field theories in manifolds with timelike boundaries within the covariant phase space program. With the recently developed relative bicomplex framework, we explore the space of solutions and presymplectic structures associated with each action principle and analyse their equivalence. The first action we consider is the Einstein-Hilbert (EH) action with the Gibbons- Hawking-York boundary term. By including the appropriate boundary terms in the variational principles, we show that the metric and tetrad formulations derived from them are equivalent. Furthermore, we show that their solution spaces are the same and that their presymplectic structures and associated charges coincide. The second action we consider is the Palatini action with the Obukhov boundary term, assuming torsion and non-metricity, and we prove the equivalence between its metric and tetrad formulations. Furthermore, we show that the metric and tetradsector of the first-order Palatini formulation are equivalent to the metric and tetrad formulations of the EH action. Lastly, we introduce the Hojman-Mukku-Sayed (HMS) action, a generalisation of the Palatini action plus the Holst term in the presence of boundaries with non-metricity and torsion. We prove that the space of solutions of the HMS and Palatini actions coincided and conclude that HMS’s metric and tetrad sectors are identical to their corresponding versions of the EH action. Additionally, we prove that the Palatini and HMS Lagrangians are not cohomologically equal despite defining the same space of solutions. Consequently, a careful analysis is required for the presymplectic structures and the charges because they may differ. However, we show that the covariant phase spaces of both theories were equivalent. This sheds light on some open problems regarding the equivalence of their associated charges in different formulations. Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid Presidente: José Navarro Salas.- Secretario: Bogar Díaz Jiménez.- Vocal: Mercedes Martín Benito

Ingeniería en Tecnologías Industriales