This course introduces quantum field theory from scratch and then develops the theory of the quantum fluctuations of fields and particles. We will focus, in particular, on how quantum fields are affected by curvature and by spacetime horizons. This will lead us to the Unruh effect, Hawking radiation and to inflationary cosmology. Inflationary cosmology, which we will study in detail, is part of the current standard model of cosmology which holds that all structure in the universe - such as the distribution of galaxies - originated in tiny quantum fluctuations of a scalar field and of space-time itself. For intuition, consider that quantum field fluctuations of significant amplitude normally occur only at very small length scales. Close to the big bang, during a brief initial period of nearly exponentially fast expansion (inflation), such small-wavelength but large-amplitude quantum fluctuations were stretched out to cosmological wavelengths. In this way, quantum fluctuations are thought to have seeded the observed inhomogeneities in the cosmic microwave background - which in turn seeded the condensation of hydrogen into galaxies and stars, all closely matching the increasingly accurate astronomical observations over recent years. The prerequisites for this course are a solid understanding of quantum theory and some basic knowledge of general relativity, such as FRW spacetimes.

https://uwaterloo.ca/physics-of-information-lab/teaching/quantum-field-theory-cosmology-amath872phys785-w2024

https://pitp.zoom.us/j/96567241418?pwd=U3I1V1g4YXdaZ3psT1FrZUdlYm1zdz09

This mini-course will introduce twisted holography, which is holography for BPS subsectors of gauge theory and gravity. We will start by introducing the B-model topological string from the space-time perspective, before discussing branes, backreaction, and the holographic duality.

Zoom: https://pitp.zoom.us/j/98839130613?pwd=SExFK0ZVYzJ3NmJhU1RFa21PWU1qQT09

The course is an introduction to quantum field theory in curved spacetime. Upon building up the general formalism, the latter is applied to several topics in the modern theory of gravity and cosmology where the quantum properties of fundamental fields play an essential role.

Topics to be covered:
1) Radiation of particles by moving mirrors 
2) Hawking radiation of black holes  
3) Production of primordial density perturbations and gravity waves during inflation
4) Statistical properties of the primordial spectra  

Required prior knowledge:
Foundations of quantum mechanics and general relativity

This course has two main goals: (1) to introduce some key models from condensed matter physics;  and (2) to introduce some numerical approaches to studying these (and other) models.  As a  precursor to these objectives, we will carefully understand many-body states and operators from  the perspective of condensed matter theory.  (However, I will cover only spin models.  We will not  discuss or use second quantization.)

Once this background is established, we will study the method of exact diagonalization and write  simple python programs to find ground states, correlation functions, energy gaps, and other  properties of the transverse-field Ising model.  We will also discuss the computational limitations  of exact diagonalization.  Finally, I will introduce the concept of matrix product states, and we will  see that these can be used to study ground state properties for much larger systems than can be  studied with exact diagonalization.

Each 90-minute session will include substantial programming exercises in addition to lecture.  Prior programming experience is not expected or required, but I would like everyone to have  python (version 3) installed on their computer prior to the first class, including Jupyter notebooks;  see “Resources” below.