Innovating Works

BVCGA

Financiado
The BV Construction a Geometric Approach
The BRST (Becchi-Rouet-Stora-Tyutin) cohomology plays a very important role in facing the problem of quantizing non-abelian gauge theories via the path integral approach. Indeed, this quantization procedure fails when applied to g... The BRST (Becchi-Rouet-Stora-Tyutin) cohomology plays a very important role in facing the problem of quantizing non-abelian gauge theories via the path integral approach. Indeed, this quantization procedure fails when applied to gauge theories, due to the presence of local symmetries in the action. This problem is overcome by introducing extra (non-physical) fields, defining a so-called BRST cohomology complex. It is precisely this cohomology that allows the recovery of important information on the theory, such as its set of observables or its renormalizability. Despite of its relevance in the context of quantum fields theory, this cohomology still deserves to be fully understood from a mathematical/geometrical point of view. As I discovered in my PhD thesis, a very promising approach to reach this goal is to try to insert the BRST cohomology (constructed following the Batalin-Vilkovisky (BV) approach) in the framework given by Noncommutative Geometry (NCG). In this project I will continue along this line of research by focusing on the case of finite-dimensional gauge theories. Indeed, this context has shown to be surprisingly rich for the analysis of the BV formalism, due to the emergence of a peculiar phenomenon, not appearing in the infinite-dimensional case: the infinite ghosts-for-ghosts. Even though since the discovery of NCG it is known its strong connection with gauge theories, the idea of using NCG as a mathematical framework to formalize the BV construction and the BRST cohomology is still an unexplored territory. The credibility of this approach has been proved by some preliminary results I obtained for U(2)-gauge theories. Moreover, since NCG gives a common tool (the notion of spectral triple) to study both finite and infinite-dimensional gauge theories, the results obtained with this project will be a fundamental starting point for further research: they will point the way to investigate the BV construction also for gauge theories on a 4-dim spacetime. ver más
28/10/2019
AU
200K€
Duración del proyecto: 31 meses Fecha Inicio: 2017-03-27
Fecha Fin: 2019-10-28

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2019-10-28
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
MSCA-IF-2016: Individual Fellowships
Cerrada hace 8 años
Presupuesto El presupuesto total del proyecto asciende a 200K€
Líder del proyecto
AARHUS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5