Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Chicago Lectures in Physics)

Rating:
Summary: Fields over Particles
Review: There is an old debate in quantum physics: Do we consider particles or waves? Some believe that debate was concluded by Wigner's work, which says *loosely* that particles are sets of quantum numbers arising as excitations of a given quantum field. The quantum field in turn is an effective structure appearing at low energies due to three fundamental properties of our world: Clustering, relativity, and basic quantum mechanics.

However, the above picture assumes regimes far from strong gravitational fields. In the case of such fields Hawking radiation, and black hole thermodynamics arise, which forces one back to the old question: Do we consider waves or particles. This plot thickens when one considers the fact that in strict general relativity global symmetries, and subsequently conserved quantities such as energy, are special cases within the space of all classical configurations. How do we then go about constructing particle quantum numbers --- which are the origin of the classical conserved quantities --- in a strongly curved circumstance?

Wald's text shows us exactly a method for doing so and more. In Wald's `QFT in Curved Spacetime and Black Hole Thermodynamics' fields are given primary status and explicit consideration of the symplectic spaces, manifolds and geometry associated with the classical space of solutions is made. As an example, the Klein Gordon scalar field is considered in detail. Having completed that task quantization in a geometric manner is possible and carried out in Rindler's geometry --- and others --- where Unruh's effect can be seen. Black hole thermodynamics is derived carefully in this text and its relation to Hawking radiation is precisely shown using all previous techniques presented in the document.

This is a text that is not served by skipping around. Everything here is truly relevant and worth the read. Wald is a true master at conveying in words the tension and solutions of GR and this text clearly describes the motivation, problems and solutions associated with QFT on curved backgrounds.