Formalismo de línea de mundo en teorías no conmutativas

La unificación de las fuerzas descriptas en el modelo estándar y gravitatoria en una teoría de la gravedad cuántica es quizás el problema más importante, desde el punto de vista teórico, a resolver por la física actual. La teoría cuántica de campos (TCC) no conmutativa (NC) se ha establecido en los últimos años como un posible modelo efectivo de la gravedad cuántica debido, fundamentalmente, a las benignas propiedades de renormalización que han demostrado tener algunos modelos dentro de este marco. El objetivo de esta tesis es la implementación de las técnicas del formalismo de línea de mundo (FLM), las cuales ya han demostrado su eficacia en el estudio de las TCC usuales, al cálculo de cantidades a un bucle de diversos modelos de TCC NC. El principal resultado consiste en el análisis a un bucle del modelo de Grosse-Wulkenhaar utilizando el FLM. Asimismo, mostramos como adaptar el FLM a modelos no conmutativos de campos escalares autointeractuantes en el plano Moyal. En el camino de esta adaptación, encontramos los desarrollos (para tiempo propio pequeño) del núcleo de calor de operadores con potenciales singulares y no locales; estos resultan de interés tanto por su posible aplicacion física como por su contenido matemático.Facultad de Ciencias Exacta

Vacuum effective actions and mass-dependent renormalization in curved space

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.Comment: 26 pages, review prepared for the special issue of Universe collecting the contributions for the workshop "Quantum Fields - from Fundamental Concepts to Phenomenological Questions" (Mainz 26-28 September 2018), covers the results of 1803.06948 and 1812.0046

Thermodynamics in the NC disc

We study the thermodynamics of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. We explicitly obtain expressions for thermodynamic potentials of gases of particles obeying different statistics. In order to do that, we derive an asymptotic expansion for the density of the zeros of Laguerre polynomials. As a result we prove that the Bose-Einstein condensation in the noncommutative disc does not take place.Instituto de Física La PlataFacultad de Ciencias Exacta

Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ *

We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix γ* in dimensional regularization, we work in n dimensions from the very beginning and use the Breitenlohner-Maison scheme to define γ*. We show that the parity-odd contribution to the trace anomaly vanishes (for which the use of dimension-dependent identities is crucial), and that the parity-even contribution is half the one of a Dirac fermion. To arrive at this result, we compute the full renormalized expectation value of the fermion stress tensor to second order in perturbations around Minkowski spacetime, and also show that it is conserved.Facultad de Ciencias Exacta

Universal definition of the non-conformal trace anomaly

We show that there exists a generalized, universal notion of the trace anomaly for theories which are not conformally invariant at the classical level. The definition is suitable for any regularization scheme and clearly states to what extent the classical equations of motion should be used, thus resolving existing controversies surrounding previous proposals. Additionally, we exhibit the link between our definition of the anomaly and the functional Jacobian arising from a Weyl transformation.Comment: 10 pages. Two comments added. Matches the published versio

Form factors and decoupling of matter fields in four-dimensional gravity

We extend previous calculations of the non-local form factors of semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case can be seen as the sum of a power series of total derivatives, but it enables us to derive the beta function of Newton's constant and formally evaluate the decoupling law in the new sector, which turns out to be the standard quadratic one.Comment: 17 pages, 2 figures; v2: improved the discussion of section

Boundaries in the Moyal plane

We study the oscillations of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. The space of quantum fluctuations of the field is finite dimensional and displays the rotational and parity symmetry of the disc. We perform a numerical evaluation of the (finite) Casimir energy and obtain similar results as for the fuzzy sphere and torus.Instituto de Física La Plat