Introduction to Quantum Field Theory in Curved Spacetime
Prerequisites, Timetable, Outline, Literature, and more ...
Summary and Overview
The main aim of this course is to explain what are (some of) the obstacles that one faces when trying to generalise the standard formalism and procedures of Minkowski space Poincare-covariant QFT to curved spacetimes, and to illustrate the new phenomena that one encounters by some typical and important examples: particle creation by time-dependent gravitational fields, the Unruh effect, and (some elementary aspects of) Hawking black hole radiation and black hole thermodynamics.Many of the key-issues can already be understood in a purely quantum-mechanical context by studying the Heisenberg picture quantisation of a time-dependent harmonic oscillator, so I will spend some time to discuss the issue of quantisation ambiguities, Bogoliubov transformations, mode creation etc., in this setting. When moving on to field theory, we will consider the simplest possible case of a free Klein-Gordon scalar field (in 1+1 or 3+1 dimensions). The general lesson is that in general in a curved spacetime the notion of vacuum and particles (and the corresponding particle interpretation of QFT) are ambiguous and observer-dependent.
We will then apply these insights to briefly look at the creation of particles in a time-dependent gravitational field, Minkowski space QFT and accelerated observers (the Unruh effect), and scalar fields in the Schwarzschild black hole metric (Hawking radiation).
Time permitting, and if there is sufficient interest, I will add a few remarks either on black hole thermodynamics, the black hole information loss paradox and the recent debate in the literature on ``firewalls'', or on more general (physically and mathematically more satisfactory) approaches to defining and making sense of quantum field theory in curved spacetime backgrounds.
Prerequisites
- Basics of Quantum Field Theory: Canonical Quantisation of Free Scalar Fields (mode expansions, creation and annihilation operators, vacuum, Fock space, ...).
- Basics of General Relativity (general formalism, proper distance and proper time, Rindler, Schwarzschild, Kruskal, simple cosmological metrics).
Schedule
- Time and Place: Wednesday 10.15 -- 13.00 Room 119
- Starting Date: Wednesday, September 21st
Outline (tentative)
- Introduction: Motivation and Overview
- Heisenberg Picture Quantum Theory of a (Time-dependent) Harmonic Oscillator
- QFT in FRW Cosmological Backgrounds and Particle Production
- Developing the Formalism
- Rindler Space and the Unruh Effect
- Aspects of the Classical Theory of Black Holes
- Hawking Radiation
- Black Hole Entropy and related Issues (if there is time)
Literature
- Monographs
- N. Birrell, P. Davies: Quantum Fields in Curved Space
- V. Mukhanov, S. Winitzki: Quantum Effects in Gravity (the first half of the course will be loosely modelled on the first half of this book)
- L. Parker, D. Toms: Quantum Field Theory in Curved Spacetime
- R. Wald: Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
- see also
- chapter 14 of R.M. Wald: General Relativity
- chapter 09 of S. Carroll: Spacetime and Geometry, an Introduction to General Relativity
- Online Lecture Notes
- R. Brout et al.: A Primer for Black Hole Quantum Physics
- L. Ford: Quantum Field Theory in Curved Spacetime
- T. Jacobson: Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect
- T. Jacobson: Black holes and Hawking radiation in spacetime and its analogues
- J. Traschen: An Introduction to Black Hole Evaporation (beware of typos)
- A. Wipf: Quantum Fields near Black Holes
- G. 't Hooft: Introduction to the Theory of Black Holes
- C. Krishnan: Quantum Field Theory, Black Holes and Holography
- J. Haro: Topics in Quantum Field Theory in Curved Space
- P.-H. Lambert, Introduction to Black Hole Evaporation
- J. Preskill: Quantum Field Theory in Curved Spacetime (1990)
- Further Information on selected topics
- Towards a mathematically more rigorous and satisfactory formulation
- B. Kay: Quantum field theory in curved spacetime
- R. Wald: The History and Present Status of Quantum Field Theory in Curved Spacetime
- R. Wald: [0907.0416] The Formulation of Quantum Field Theory in Curved Spacetime
- S. Hollands, R. Wald: [0803.2003] Axiomatic quantum field theory in curved spacetime
- M. Benini, C. Dappiaggi, T. Hack, [1306.0527] Quantum Field Theory on Curved Backgrounds -- A Primer
- S. Holland, R. Wald, [1401.2026] Quantum fields in curved spacetime
- T. Hack, Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes
- The Unruh Effect
- For a detailed review, with many references, see
L. Crispino et al: The Unruh effect and its applications - Hawking Radiation and Classical and Quantum Black Hole Thermodynamics
- L. Susskind, J. Lindesay: Black Holes, Information and the String Theory Revolution
- J. Bardeen, B. Carter, S. Hawking: The Four Laws of Black Hole Mechanics
- S. Hawking: Particle Creation by Black Holes
- S. Hawking: The Nature of Space and Time
- G. Gibbons: An Introduction to Black Hole Thermodynamics (pdf-file and ps-file of hand-written notes available at the bottom of the page, highly recommended)
- P. Townsend: Black Holes (highly recommended)
- R. Wald: The Thermodynamics of Black Holes (highly recommended)
- R. Wald: Black Holes andThermodynamics
- D. Page: Hawking Radiation and Black Hole Thermodynamics (see section 1 for a detailed account of the history of Hawking's discovery)
- T. Jaocbson: Introductory Lectures on Black Hole Thermodynamics (ps-file, highly recommended)
- S. Ross: Black hole thermodynamics
- S. Carlip: Black Hole Thermodynamics and Statistical Mechanics
- S. Carlip: Black Hole Thermodynamics
- K. Umetsu: Recent Attempts in the Analysis of Black Hole Radiation
- T. Jacobson, D. Marolf, C. Rovelli: Black hole entropy: inside or out? (a trialogue)
- A skeptical and critical analysis (mainly on account of the so-called trans-Planckian problem) is given by
A. Helfer: Do black holes radiate? and Black holes reconsidered
(not sure what to make of this, best to form your own opinion) - General Analysis and Universality of Hawking-like Radiation
- M. Visser: Essential and inessential features of Hawking radiation
- C. Barcelo, S. Liberati, S. Sonego, M. Visser, Minimal conditions for the existence of a Hawking-like flux
- C. Barcelo, S. Liberati, S. Sonego, M. Visser, Hawking-like radiation from evolving black holes and compact horizonless objects
- Black holes and information loss paradox
- J. Polchinski: The Black Hole Information Problem
- A. Strominger: Les Houches Lectures on Black Holes
- S. Mathur: What Exactly is the Information Paradox? (highly recommended)
- S. Mathur: The information paradox: A pedagogical introduction
- S. Mathur: What the information paradox is not
- S. Mathur: The information paradox: conflicts and results
- Firewalls
- Ahmed Almheiri, Donald Marolf, Joseph Polchinski, James Sully, Black Holes: Complementarity or Firewalls?
- Ahmed Almheiri, Donald Marolf, Joseph Polchinski, Douglas Stanford, James Sully, An Apologia for Firewalls
- J. Polchinski: The Black Hole Information Problem
- Matthias Blau, Office 220a
Most of the lecture notes listed above discuss this to a certain extent. For further information see e.g. Part I of the monograph
Recently, the debate about the untarity of black hole evaporation and its compatibility with black hole complementarity (and the equivalence principle) has been reignited by the firewall proposal in the articles below:
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