Freestyle introductory summer course on the first and second quantization of identical particles, for physicist (BSc,) MSc, and PhD students.
This course is under construction. Following the detailed description of the symmetric and antisymmetric subspace of the tensor power, and the Fock space in the case of finite number of modes, the main goal is to cover some important notions of correlation and entanglement in the particle (first quantization) and mode (second quantization) pictures.
The material is built upon the course 'Quantum entanglement 2023 spring'.

Topics planned to be covered:

Course Information

• This course is completely unofficial.
• Lecturer: Szilárd Szalay, e-mail: szalay.szilard (at) wigner (dot) hu
• Location: mostly online (email me if interested) or Wigner RCP, Building I., first floor, conference room sometimes
• Time: Tuesdays, 16:00-17:30
• The language of the course will be Hungarian, if every attendant speaks that.

Information, announcements

• The lectures of Milán Mosonyi, Péter Vrana and Attila Andai (Mathematical Institute, BUTE) are highly recommended for those who like quantum mechanics in a more rigorous treatment (also in infinite dimensions, with functional analysis), and for those who would like to get more quantum information theory than given in the present lectures.
• For those who are intereted in quantum foundations, the reading seminar led by Gábor Hofer-Szabó is strongly recommended. (See further announcements there.)
• (for myself: Neptun BUTE, timetable BUTE, timetable ELTE)
• 1st. lecture, on the 18th July (online): preliminaries (distinguishable systems), symmetric and antisymmetric subspace (scalar product, norm).
• 2nd. lecture, on the 25th July (online): bosons/fermions (first quantization of insidtinguishable systems), symmetric and antisymmetric subspace 2 (permutations, representation, bases), examples.
• 3rd. lecture, on the 10th of August (online): CCR/CAR algebra of creation and annihilation operators (first quantized case).
• 4th. lecture, on the 29th of August (online): examples.
• 5th. lecture, on the 5th of September (online): operator extension and state reduction (distinguishable systems, first quantization of insidtinguishable systems) in general and by creation and annihilation operators.
• 6th. lecture, on the 28th of September (online): occupation number representation, second quantization, Jordan-Wigner representation of CAR algebra.
• (7th. lecture, planned (online): maps on CCR/CAR algebras (Bogoliubov transformations, mode transformations))

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