BVCGA · The BV Construction: a Geometric Approach
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2017-05-01 → 2019-10-28
- EU contribution
- €200,195
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
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Results in brief
The BV Construction: a Geometric Approach
Nowadays, physics is taking gigantic steps in decoding the deep structure of the world: particle accelerators and advanced detectors have finally verified theoretical predictions, of which the Higgs boson and gravitational waves are monumental. Nevertheless, many aspects of nature are still mysterious, such as the quantization of gauge theories. Historically, the concept of quantization was introduced at the beginning of the 20th century, when physicists discovered that the behavior of particles is ruled by probabilistic laws. However, even if more than a century has passed, we are still searching for a (mathematically rigorous) method to quantize a crucial class of theories, called gauge theories. What makes solving this problem so important is that, mathematically, all fundamental interactions, such as the gravitational or the electromagnetic ones, are governed by this type of theories. Over the years, several attempts have been made to solve this problem. Lately, the BV (Batalin-Vilkovisky) quantization procedure proved to be a good candidate. Within this scenario, my research aims to find a new geometric formulation of the BV construction, within the framework of a recently developed mathematical theory called noncommutative geometry. Even though the deep relation existing between gauge theories and noncommutative geometry, by the means of its key notion of spectral triple, has always been evident, the possibility of using this mathematical language to investigate the geometric meaning of the BV construction was still highly unexplored when I started this project. But now, I proved that by approaching the BV quantization procedure from the prospective of noncommutative geometry, one opens completely new scenarios.
Data: CORDIS, © European Union
Project objective
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.
Original text from CORDIS.
Participants
- AARHUS UNIVERSITET · Aarhus CCoordinatorDenmark
Links
Data: CORDIS, © European Union