Níck

theoretical physicist

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Functional Renormalization Group

“Renormalization group” is a fancy name we give to understanding how theories change with scale. Theories in larger scales don’t need to be treated with all of the details found in smaller scales. For example, when describing the motion of the ocean, it is usually unnecessary to consider the molecular structure of water. The renormalization group helps us to do this “zoom-out” procedure within the framework of quantum field theories. “Functional renormalization group,” in turn, is the name given to some nonperturbative incarnations of the renormalization group. It then consists of a technique to obtain information about a theory that goes beyond the typical approximations done in physics.

One interesting application of this tool is the asymptotic safety program in quantum gravity. Quantum general relativity is problematic at high energies because it is a non-renormalizable theory. However, it may be that this is an issue not with the theory itself, but rather with the perturbative approximation usually employed when studying it. The FRG allows one to study quantum gravity in a non-perturbative fashion, hence gathering information that otherwise would not be available. In the non-perturbative sense, a quantum field theory of gravity may be renormalizable after all.

Further Reading

The following references discuss the functional renormalization group, often with a view toward quantum gravity and quantum field theory in curved spacetime.

• Aguiar Alves, Níckolas de. “Nonperturbative Aspects of Quantum Field Theory in Curved Spacetime.” MSc thesis, Federal University of ABC, 2023. arXiv: 2305.17453 [gr-qc].
• Codello, Alessandro. “A Novel Functional Renormalization Group Framework for Gauge Theories and Gravity.” PhD dissertation, Johannes Gutenberg-Universität Mainz, 2010.
• Delamotte, Bertrand. “An Introduction to the Nonperturbative Renormalization Group.” In Renormalization Group and Effective Field Theory Approaches to Many-Body Systems, edited by Janos Polonyi and Achim Schwenk, pp. 49–132. Lecture Notes in Physics 852. Berlin: Springer, 2012. arXiv: cond-mat/0702365.
• Kopietz, Peter, Lorenz Bartosch, and Florian Schütz. Introduction to the Functional Renormalization Group. Lecture Notes in Physics 798. Berlin: Springer, 2010.
• Percacci, Roberto. An Introduction to Covariant Quantum Gravity and Asymptotic Safety. 100 Years of General Relativity 3. Singapore: World Scientific, 2017.
• Reuter, Martin, and Frank Saueressig. Quantum Gravity and the Functional Renormalization Group: The Road Towards Asymptotic Safety. Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press, 2018.

My Publications on and Around This Topic

• Aguiar Alves, Níckolas de (2023). “Nonperturbative Aspects of Quantum Field Theory in Curved Spacetime”. MSc thesis. Santo André, Brazil: Federal University of ABC. xxiv, 152 pp. arXiv: 2305.17453 [gr-qc]. Summarized here.