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Bernabeu, J., & Navarro-Salas, J. (2019). A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited. Symmetry-Basel, 11(10), 1191–13pp.
Abstract: A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov-Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner.
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Ramirez-Uribe, S., Hernandez-Pinto, R. J., Rodrigo, G., & Sborlini, G. F. R. (2022). From Five-Loop Scattering Amplitudes to Open Trees with the Loop-Tree Duality. Symmetry-Basel, 14(12), 2571–14pp.
Abstract: Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N7MLT universal topology, that allows us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.
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Navarro-Salas, J., & Pla, S. (2022). Particle Creation and the Schwinger Model. Symmetry-Basel, 14(11), 2435–9pp.
Abstract: We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage of the fact that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem by following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results match exactly in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with a previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime.
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Fioresi, R., & Lledo, M. A. (2021). Quantum Supertwistors. Symmetry-Basel, 13(7), 1241–16pp.
Abstract: In this paper, we give an explicit expression for a star product on the super-Minkowski space written in the supertwistor formalism. The big cell of the super-Grassmannian Gr(2|0,4|1) is identified with the chiral, super-Minkowski space. The super-Grassmannian is a homogeneous space under the action of the complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4, signature (1,3), and supersymmetry N=1. The quantization is done by substituting the groups and homogeneous spaces by their quantum deformed counterparts. The calculations are done in Manin's formalism. When we restrict to the big cell, we can explicitly compute an expression for the super-star product in the Minkowski superspace associated to this deformation and the choice of a certain basis of monomials.
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Lledo, M. A. (2020). Superfields, Nilpotent Superfields and Superschemes dagger. Symmetry-Basel, 12(6), 1024–32pp.
Abstract: We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. We study the non-trivial relation of scalar superfields with the defining sheaf of the supermanifold of super spacetime. We also investigate in the present work some constraints that are imposed on the superfields, which allow for non-trivial solutions. They give rise to superschemes that, generically, are not regular, that is they do not define a standard supermanifold.
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