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BVCGA

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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... see more

28/10/2019

200K€

Project Budget: 200K€

Project leader

AARHUS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

PARTICIPATION DEPralty Sin fecha límite de participación.

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Financing granted El organismo H2020 notifico la concesión del proyecto The day 2019-10-28

MSCA-IF-2016: Individual Fellowships Objective:The goal of the Individual Fellowships is to enhance the creative and innovative potential...

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2 Participantes

200.19K€ | Leader

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989.70K€ | participant

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Project duration: 31 months Date Start: 2017-03-27
End date: 2019-10-28

Project leader

AARHUS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Project Budget 200K€

participation deadline Sin fecha límite de participación.

Project description 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.

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