Download Quantum Field Theory and Functional Integrals pdf by Nima Moshayedi, These notes describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the most focus lies in euclidean field theory. The notion of gaussian measure and therefore the construction of the Wiener measure are covered. Download the pdf from below to explore all topics and start learning.


Part 1. A Brief Recap of Classical Mechanics
2. Newtonian Mechanics with examples
2.1. Conservation of Energy
3. Hamiltonian Mechanics
3.1. The general formulation
3.2. The Poisson bracket
4. Lagrangian Mechanics
4.1. Lagrangian system
4.2. Hamilton’s least action principle
5. The Legendre Transform

Part 2. The Schrödinger Picture of Quantum Mechanics
6. Postulates of Quantum Mechanics
6.1. First Postulate
6.2. Second Postulate
6.3. Third Postulate
6.4. Summary of CM and QM
7. Elements of Functional Analysis
7.1. Unbounded operators
7.2. Adjoint of an unbounded operator
7.3. Quantization of a classical system
7.4. More on self adjoint operators
7.5. Eigenvalues of single Harmonic Oscillator
7.6. Weyl Quantization on R2n
8. Solving Schrödinger equations, Fourier Transform and Propagator
8.1. Solving the Schrödinger equation
8.2. The Schrödinger equation for the free particle moving on R
8.3. Solving the Schrödinger equation with Fourier Transform

Part 3. The Path Integral Approach to Quantum Mechanics
9. Feynman’s Formulation of the Path Integral
9.1. Free Propagator for the free particle on R
10. Construction of the Wiener measure
10.1. Towards nowhere differentiability of Brownian Paths
10.2. The Feynman-Kac Formula
11. Gaussian Measures
11.1. Gaussian measures on R
11.2. Gaussian measures on finite dimensional vector spaces
11.3. Gaussian measures on real seperable Hilbert spaces
11.4. Standard Gaussian measure on H
12. Wick ordering
12.1. Motivating example and construction
12.2. Wick ordering as a value of Feynman diagrams
12.3. Abstract point of view on Wick ordering
13. Bosonic Fock Spaces

Part 4. Construction of Quantum Field Theories
14. Free Scalar Field Theory
14.1. Locally convex spaces
14.2. Dual of a locally convex space
14.3. Gaussian measures on the dual of Fréchet spaces
14.4. The operator (∆ + m2)−1
15. Construction of self interacting theory
15.1. More random variables
15.2. Generalized Feynman diagrams
15.3. Theories with exponential interaction
15.4. The Osterwalder-Schrader Axioms
16. QFT as operator valued distribution
16.1. Relativistic quantum mechanics
16.2. Garding-Wightman formulation of QFT