What you'll learn
Quantization of Gravity in Weak Gravitational Fields: Learn the fundamental principles behind the quantization of gravity within the framework of QFT
Derive and Understand Classical and Quantum Aspects of Gravity: Step-by-step derivation of classical and quantum aspects of gravity
Probability to find gravitons
Solve Equations for a Massless Spin-2 Field
Apply Path Integral and Partition Function in Quantum Gravity
Quantify Gravitons Using QFT
Interpret Polarization of Gravitational Waves
Derive properties of tensors and familiarize with them by doing step-by-step calculations
Perturbations of the metric tensor
Inverse metric tensor expressed as a perturbation series
Ricci tensor expressed as a perturbation series
Determinant of the metric tensor expressed as a perturbation series

Requirements
Strong Foundation in Tensor Calculus
knowledge of Einstein field equations
Quantum Field Theory Background: prior exposure to quantum field theory, especially in the language of path integrals
Understanding of Complex Calculus (in particular, the Residue Theorem)

Description
The particles we encounter in nature, whether massive or massless, experience the gravitational interaction due to their energy content. Although gravitational interactions are way smaller than other interactions in nature, the incorporation of gravity in quantum interactions seems important (for example in the description of our early universe or black hole physics).You might hear people addressing the incompatibility between quantum physics and general relativity, as well as the need to make efforts in order to find the desired theory of Quantum Gravity.Sometimes you might hear people refer to String Theory, some other times to Loop Quantum Gravity. These theories have opened up new ways of looking at reality, for sure, but we might still be a long way from being able to test them.On the other hand, under certain circumstances, it is already possible to quantize gravity, by using the well-known quantum field theory approach. This is possible only when we are dealing with weak gravitational fields.In this course, we will see how the concept of graviton emerges quite naturally by considering small deviations of the metric tensor from flat spacetime.In particular, we will start from Einstein field equations of General Relativity, and we will assume that the metric tensor is a small perturbation of the Minkowski metric.From there, we will derive Einstein field equations up to second order of the perturbation.We will see that the equations derived in this way are those of a massless spin-2 field.After that, we proceed to solve the equations and find a way to express the metric tensor.After dealing with the classical equations, we switch to the quantum realm by quantizing the field, recalling the concept of path integral and partition function. The quantum theory will allow us to derive the average number of gravitons and understand the concept of polarization of gravitational waves.In all the derivations it is assumed that the student is familiar with tensor calculus, Einstein field equations, quantum field theory in the language of path integrals, complex calculus. Therefore, it goes without saying that the course is aimed at students who master these concepts. On the other hand, the equations will be derived step by step, leaving the time to digest the concepts.