Math Intuition for Quantum Mechanics & Quantum Field Theory

Quantum Mechanics and Quantum Field Theory

The mathematical intuition for Quantum Mechanics and Quantum field theory

How to (intuitively) derive the Schrodinger's equation from the classical theory

Quantum operators

Quantum states

Importance of commutators

Derivation of Heisenberg Uncertainty Principle

Unitary operators

How to quantize a Classical Field theory

Klein Gordon equation

Wick's theorem

ordering

Normal ordering

Noether's theorem

Properties of the infinitesimal Lorentz transformation

Spectrum of the Hamiltonian

Scattering cross-section

Annihilation and creation operators

Causality in quantum field theories

Ground state

Green functions

Schrodinger's picture

Heisenberg's picture

Interaction picture

Theory of Fermions

Theory of Bosons

Dirac equation

Interacting Field theory

Feynman diagrams

Anomalous magnetic moment

Special Relativity (for Quantum Field Theory)

Fourier Series and Transforms

Multivariable Calculus

Tensors (for Quantum Field Theory)

Complex calculus (for Quantum Field Theory)

Classical Physics

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This course aims to mathematically motivate both Quantum Mechanics (QM) and Quantum field Theory (QFT). The first part is devoted to the most important concepts and equations of QM, whereas the second part deals with QFT.

Due to the conceptual and mathematical difficulty of these subjects, some prerequisites to this course are unavoidably required. The student should be familiar with:

1) the Fourier Series and Transform;

2) Multivariable Calculus;

3) Probability theory and random variables;

4) Classical Physics;

5) Complex Calculus (especially residues and calculation of integrals on a contour), although this is necessary only for some parts of the course devoted to QFT;

6) Special Relativity and tensors for QFT.

Note 1: the first few prerequisites might be enough if you are interested only in the first part of the course, which is related to QM (consider that this course has tens of hours' worth of material, you might be interested only in some parts);

Note 2: I'm more than willing to reply if you have doubts/need clarifications, or -why not- have any recommendations to improve the quality of the course.

Note 3: I'll still keep editing the videos (for example by adding notes) to make the video-lectures as clear as possible.

The references for the part on QFT are the following:

- Quantum Field Theory, M.Srednicki

- Quantum Field Theory, Itzykson & Zuber

- QFT by Mandl & Shaw

- QFT in a nutshell, A.Zee

- QFT by Ryder, Ramand

- The Quantum Theory of Fields, S.Weinberg

- Gauge Theories in Particle Physics, Aitchison & Z.Hey

Students who desire to develop mathematical intuition for Quantum mechanics and Quantum Field theory



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