QFT in curved spacetime: Hawking radiation, Unruh effect

QFT in curved spacetime: Hawking radiation, Unruh effect free download

Quantum Field Theory in curved spacetime, Hawking radiation, Unruh effect, quantum corrections to General Relativity

This advanced course examines the interface of quantum field theory (QFT) and general relativity, focusing on the theoretical and mathematical structures that govern quantum fields in curved spacetime. The course is intended for graduate students, researchers, as well as professionals in theoretical physics.

The syllabus includes the following key topics (not necessarily in this order):

1. Foundations of QFT in Curved Spacetime

   • Definition of quantum fields in non-Minkowskian geometries.

   • Vacuum states, particle creation, and the semiclassical approach.

2. Hawking Radiation

   • Derivation and analysis of black hole radiation.

   • Implications for black hole thermodynamics and entropy.

   • Black hole lifetime and evaporation processes

   • Insights from the holographic principle and Loop Quantum Gravity

3. The Unruh Effect

   • Examination of vacuum fluctuations as perceived by uniformly accelerated observers.

   • Theoretical connection to the Rindler horizon and thermal effects.

   • Rindler and Minkowski vacua, and the role of Bogolyubov coefficients

   • Connection between acceleration, temperature, and entropy

4. Mathematical Framework for the Calculation of Quantum Corrections to Gravity

   • Path integral formulation and its application to curved spacetime

   • Heat kernel methods, zeta function regularization, and renormalization

   • Euclidean quantum gravity and effective action approaches

   • Lorentz and Poincaré group representations in curved spacetime

5. Applications to Quantum Gravity & Cosmology

   • Quantum corrections to General Relativity from effective field theory

   • Scalar fields in expanding universes and inflationary models

   • Casimir force, semiclassical gravity, and emergent spacetime models

By the end of the course, students will develop a thorough understanding of the core theoretical principles of QFT in curved spacetime, as well as their implications for fundamental physics. The course will equip participants with the tools necessary to engage in more advanced research in quantum gravity, black hole physics, and cosmology.

Prerequisites:
Participants should have a solid foundation in QFT and general relativity. Familiarity with advanced mathematical methods, including functional analysis and differential geometry, is strongly recommended. However, the first section recalls those relevant concepts of QFT, which are used extensively throughout the course.

Course Format:
The course is structured around "formal" lectures (aiming to stimulate physical and mathematical intuition), and critical discussions of seminal and contemporary research literature. It aims to provide a rigorous and comprehensive understanding of the subject.