Geometry Elective 1 - NMAG496 (Beyond GR: a catalogue of theories of quantum gravity)

• Title: Výběrová přednáška z geometrie 1
• Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2022
• Semester: winter
• E-Credits: 3
• Hours per week, examination: winter s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: Eugenia Boffo, Ph.D.
• Class: M Mgr. MSTR; M Mgr. MSTR > Volitelné
• Classification: Mathematics > Geometry

Annotation

English

Last update: Mgr. Dalibor Šmíd, Ph.D. (16.06.2021)

Reconciling GR with quantum field theory is the mantra of our century, but besides the most famous candidates theories of quantum gravity, i.e. string/M-theory and loop quantum gravity, there are also some promising proposals in other directions. The aim of this course is to shed light on some of these less-known models of gravity addressing their theoretical foundations and highlighting the problems they solve and the questions they leave open.

Czech

Last update: Mgr. Dalibor Šmíd, Ph.D. (16.06.2021)

Sladění obecné teorie relativity s kvantovou teorií pole je mantrou našeho století, ale kromě nejznámějších kandidátů na teorie kvantové gravitace, tj. teorie strun/M-teorie a smyčkové kvantové gravitace, existují také slibné návrhy v jiných směrech. Cílem tohoto kurzu je osvětlit některé z těchto méně známých modelů gravitace, přičemž se budeme zabývat jejich teoretickými základy, problémy, které řeší, i otázkami, které ponechávají otevřené.

Aim of the course

Last update: Eugenia Boffo, Ph.D. (19.09.2021)

The purpose of the course is to understand why the more common quantization techniques do not work with Einstein's theory of gravity, and to critically analyse some of the less mainstream proposals for a quantum theory of gravity (Asymptotically Safe GR, Causal Dynamical Triangulations, Double Copy, Supergravity, BV-BFV of GR). Focusing more on the foundations of the proposals than the methods and the details of the calculations, the students will appreciate the various efforts perpetuated by the hep-th community for finding a renconciliation between GR and the quantum world. Towards the end, attention is also given to Quantum Fields in curved spacetimes, and briefly to String Theory (which is the most consistent UV completed theory with a spin-2 field available for now) and Loop Quantum Gravity.

Course completion requirements

Last update: Eugenia Boffo, Ph.D. (30.09.2021)

A written exam will be held at the end of the course. The successful candidate is expected to recall the main features of each quantum gravity proposals, and to know in more detail one of her/his choice. Individual discussion of the exam follows afterwards.

Literature

Last update: Eugenia Boffo, Ph.D. (19.10.2021)

General: Buchbinder, Shapiro - "Introduction to Quantum Field Theory with Applications to Quantum Gravity" (Oxford University Press, 2021), Kiefer - "Quantum Gravity" (Oxford University Press, 2007)

1-loop renormalizability: 't Hooft, Veltman -"One loop divergences in the theory of gravitation" (Ann.Inst.H.Poincare Phys.Theor.A 20 (1974) 69-94)

2-loops: Goroff, Sagnotti - "The Ultraviolet behaviour of Einstein Gravity" (Nucl.Phys.B 266 (1986) 709-736)

Asymptotic Safety in Hilbert-Einstein: Lauscher, Reuter - "Ultraviolet fixed point and generalized flow equation of quantum gravity" (Phys.Rev.D, 65, 025013,(review article) Eichhorn - "Asymptotically Safe Gravity" (contribution to ISSP 2019)

Criticism: Shomer - "A pedagogical explanation for the non-renormalizability of gravity" (arXiv:0709.3555), Donoghue - "A critique of the Asymptotic Safety Program" (Frontiers in Physics,doi: 10.3389/fphy.2020.00056)

Loll - "Quantum Gravity from Causal Dynamical Triangulations: A Review" (Class.Quant.Grav. 37 (2020) 1, 013002)

Borsten, Jurco, Kim, Macrelli, Saemann, Wolf - "BRST-Lagrangian Double Copy of Yang–Mills Theory" (Phys.Rev.Lett. 126 (2021) 19, 191601)

Teaching methods

Last update: Eugenia Boffo, Ph.D. (30.09.2021)

Blackboard class with occasional seminars.