Berezin The Method Of Second Quantization Djvu 11
Matty Fiedler
Berezin's Method of Second Quantization
The method of second quantization is a powerful mathematical tool for describing many-body quantum systems, such as electrons in atoms, molecules, and solids. It was developed by the Soviet mathematician and physicist F. A. Berezin (1931-1980) in his book The Method of Second Quantization, published in 1966. The book was translated into English by Nobumichi Mugibayashi and Alan Jeffrey in 1966.
In the method of second quantization, the wave functions are also expressed in terms of operators. The formalism starts with the introduction of an abstract vector space, the Fock space. The basis vectors of the Fock space are occupation number vectors, with each vector defined by a set of occupation numbers (0 or 1 for fermions, non-negative integers for bosons) that specify how many particles occupy each single-particle state. The operators that act on the Fock space are called creation and annihilation operators, which add or remove particles from a given state. These operators satisfy certain commutation or anticommutation relations, depending on whether the particles are bosons or fermions.
The method of second quantization allows one to write the Hamiltonian and other observables of a many-body system in a compact and elegant way, using the creation and annihilation operators. It also facilitates the calculation of various physical quantities, such as energy levels, transition probabilities, correlation functions, etc., using techniques such as perturbation theory, diagrammatic methods, Green's functions, etc.
The method of second quantization has been widely applied to various fields of physics, such as atomic physics, molecular physics, solid state physics, nuclear physics, quantum field theory, quantum optics, quantum information, etc. It is also closely related to other mathematical concepts, such as tensor products, Hilbert spaces, operator algebras, etc.
The book by Berezin is considered a classic and authoritative reference on the method of second quantization. It covers both the general theory and some specific applications to fermionic and bosonic systems. It also contains some original results by Berezin himself, such as the introduction of supermanifolds and Grassmann variables. The book is available in djvu format online, as well as in print from various libraries.
References:
- Berezin, F. A. (1966). The Method of Second Quantization. New York: Academic Press.
- Berezin, F. A., Mugibayashi, N., & Jeffrey, A. (1966). The Method of Second Quantization [DJVU]. E-book library.
- SpringerLink. (n.d.). The Method of Second Quantization.
- Internet Archive. (2019). The method of second quantization : Berezin, F. A. (Feliks Aleksandrovich) : Free Download, Borrow, and Streaming : Internet Archive.
- Library Hub. (n.d.). Item Display Library Hub.