Overview

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):Foundations of QFT in Curved SpacetimeDefinition of quantum fields in non-Minkowskian geometries.Vacuum states, particle creation, and the semiclassical approach.Hawking RadiationDerivation and analysis of black hole radiation.Implications for black hole thermodynamics and entropy.Black hole lifetime and evaporation processesInsights from the holographic principle and Loop Quantum GravityThe Unruh EffectExamination 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 coefficientsConnection between acceleration, temperature, and entropyMathematical Framework for the Calculation of Quantum Corrections to GravityPath integral formulation and its application to curved spacetimeHeat kernel methods, zeta function regularization, and renormalizationEuclidean quantum gravity and effective action approachesLorentz and Poincaré group representations in curved spacetimeApplications to Quantum Gravity & CosmologyQuantum corrections to General Relativity from effective field theoryScalar fields in expanding universes and inflationary modelsCasimir force, semiclassical gravity, and emergent spacetime modelsBy 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.

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