Aspects of regularization in quantum field theory in curved spacetimes

• Název práce v češtině: Aspekty regularizace v kvantové teorii pole v zakřivených prostoročasech
• Název v anglickém jazyce: Aspects of regularization in quantum field theory in curved spacetimes
• Klíčová slova: kvantové teorie pole|zakřivené prostoročasy
• Klíčová slova anglicky: quantum field theory|curved spacetimes
• Akademický rok vypsání: 2023/2024
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Ústav teoretické fyziky (32-UTF)
• Vedoucí / školitel: Dr. Dražen Glavan, Ph.D.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 13.05.2024
• Datum zadání: 13.05.2024
• Datum potvrzení stud. oddělením: 13.05.2024
• Konzultanti: Alexander Vikman

Zásady pro vypracování

The first part of the project will be devoted to introducing the student to the basic concepts of quantum field theory (QFT) in curved spacetimes. The emphasis will be on cosmological spacetimes and the phenomenon of gravitational particle production (Ref. [1,2]). This mostly concerns free (non-interacting) QFT on expanding backgrounds. The second part of the project will involve more advanced concepts of QFT in curved spacetimes. This will introduce the student to some of the current problems researchers face when computing quantum loop corrections to cosmological observables in the early Universe.

QFT observables in curved spacetimes exhibit more intricate divergence issues than ones known from Minkowski spacetime. Multiple methods of regularizing these divergences exist. In this project, the student will examine connections between different regularization methods for computing expectation values in cosmological QFT. Namely, the student will examine the recently reported freedom and ambiguities (Refs. [3,4,5]) in the "adiabatic regularization" scheme that is well adapted to cosmology. This regularization scheme involves subtracting the contributions of ultraviolet modes from the mode functions of the quantum field. This freedom in adiabatic regularization will be compared and contrasted to the known renormalization scheme ambiguities in dimensional regularization, with the goal of relating the two methods. This will help understand the apparent disagreements between different computations. Different manners in which the conformal anomaly arises in different schemes will also be examined. If time permits cosmological implications of backreacting fields will also be considered.

Seznam odborné literatury

[1] V. Mukhanov, S. Winitzki, "Introduction to quantum effects in gravity", Cambridge University Press, 2007, DOI:https://doi.org/10.1017/CBO9780511809149
[2] L. Parker, D. Toms, "Quantum Field Theory in Curved Spacetime", Cambridge University Press, 2009, DOI:10.1017/CBO9780511813924
[3] A. Ferreiro, F. Torrenti, "Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes", Phys.Lett.B 840 (2023) 137868, DOI:10.1016/j.physletb.2023.137868, arXiv:2212.01078 [gr-qc]
[4] A. Ferreiro, S. Monin, F. Torrenti, "Physical scale adiabatic regularization in cosmological spacetimes," Phys.Rev.D 109 (2024) 4, 045015, DOI:10.1103/PhysRevD.109.045015, arXiv:2311.08986 [gr-qc]
[5] A. Ferreiro, J. Navarro-Salas, "Running couplings from adiabatic regularization," Phys. Lett. B 792 (2019), 81-85, DOI:10.1016/j.physletb.2019.03.026, arXiv:1812.05564 [gr-qc].

Předběžná náplň práce v anglickém jazyce

This project will introduce the student to the field of nonequilibrium QFT in cosmological spacetimes that is rapidly becoming indispensable in studies of the early Universe. In fact, the quantum fluctuations during the period of primordial inflation are believed to be the source of the famed temperature fluctuations in the cosmic microwave background. Further rapid advances of modern cosmology are opening up the possibility to probe not only particle physics lying beyond the well-established standard model but also in perturbative quantum gravity by studying quantum effects in the extreme conditions of the early expanding Universe. During the first stage of this project, the student will be introduced to the basic concepts of QFT in expanding cosmological spacetimes and to the effect of gravitational particle production. During the second stage, the student will apply the acquired knowledge to study different regularization methods for ultraviolet-divergent quantities in cosmological spacetimes, and the connections between different methods. The student will work closely with the supervisor, and in addition will have the opportunity to interact with the members of the Central European Institute for Cosmology and Fundamental Physics (CEICO) of FZU, and to attend regular seminars and journal club meetings there.