Conformal Field Theory

This is the "internship report" for the first year of a master's degree in theoretical physics of fundamental interactions, the subject of which was the study (learning) of conformal field theory during four weeks (February 2025).

The document(s) has/have been written with Typst, there is a version in the original language, French, and a version translated into English. The repo also includes the PDF presentation, in the form of slides, also created with Typst.

From Wikipédia,

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.

Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points.

I'm putting this online because I think it's an interesting way of illustrating Typst's capabilities, but also because I think the document(s) could be useful to anyone who wants to learn conformal field theory. In my view, the prerequisites are as follows:

Group theory, lie algebra and representation theory on vector spaces ;
Ideas on statistical physics (in particular phenomenology, phase transitions, partition functions, phase transitions, etc.) ;
Quantum mechanics (important concepts and ideas, states, operators, etc.), basic quantum field theory ;
Concepts of analytical mechanics (Lagrangians, Hamiltonians, actions, symmetries, etc.)

In principle, the rest of the document should be self-contained.

License

vanaur/CFT

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