Second Quantization

second quantization

[′sek·ənd ‚kwän·tə′zā·shən]
(quantum mechanics)
A procedure in which the dependent variables of a classical field or a quantum-mechanical wave function are regarded as operators on which commutation rules are imposed; this produces a formalism in which particles may be created and destroyed.

Quantization, Second

 

a method used in quantum mechanics and quantum field theory to study systems consisting of many or an infinite number of particles (or quasiparticles). In this method the state of a quantum system is described by means of occupation numbers—quantities that characterize the average number of particles in a system in each possible state.

The method of second quantization is particularly important in quantum field theory when the number of particles in a given physical system is not constant but may change during various processes that transpire in the system. Therefore, quantum radiation theory and quantum theory of elementary particles and systems of various quasiparticles are the most important areas of application of the method of second quantization. Systems containing light quanta (photons), the number of which changes during the processes of emission, absorption, and scattering, are examined in radiation theory. In the theory of elementary particles the necessity of using the method of second quantization is connected with the possibility of mutual transformations of particles—for example, the processes of conversion of electrons and positrons into photons, and the reverse process. The method of second quantization is most effective in quantum electrodynamics—the quantum theory of electromagnetic processes, as well as in solid-state theory, which is based on the concept of quasiparticles. The use of second quantization is less effective for describing mutual transformations of particles caused by nonelec-tromagnetic interactions.

In the mathematical apparatus of second quantization, the wave function of a system is taken to be a function of the occupation numbers. Here the primary role is played by “creation” and “annihilation” operators of particles. The annihilation operator is an operator under whose influence the wave function of some state of a given physical system is converted into the wave function of another state having one less particle. Similarly, the creation operator increases the number of particles in the state by 1.

The fundamental aspect of the method of second quantization does not depend on whether the particles of the system conform to Bose-Einstein statistics (for example, photons) or Fermi-Dirac statistics (electrons and positrons). The specific mathematical apparatus of the method, including the main properties of the creation and annihilation operators, differs significantly in these cases because the number of particles that may exist in a given state is in no way limited in Bose-Einstein statistics (so that the occupation numbers may assume arbitrary values), whereas in Fermi-Dirac statistics no more than one particle may be in each state (and the occupation numbers may have only the values 0 and 1).

The method of second quantization was first developed by the English physicist P. Dirac (1927) in his theory of radiation; and further work was done by the Soviet physicist V. A. Fok (1932). The term “second quantization” appeared because the method developed after “ordinary,” or “first,” quantization, the purpose of which was to determine the wave properties of particles. The necessity of systematic consideration of the corpuscular properties of fields as well (since particle-wave duality is inherent in all types of matter) led to the appearance of methods of second quantization.

References in periodicals archive ?
If [mathematical expression not reproducible] falls into the second quantization interval, the resulting bits is 01.
Topics range from analyzing mathematical properties of graph polynomials to applying the polynomials in several application areas, including discussion of the interlace polynomial, independence polynomials of k-trees and compound graphs, new aspects of the Abelian sandpile model on graphs and their polynomials, second quantization of recurrences, the matching polynomial, the permanental polynomials of graphs, the general graph homomorphism polynomial, derivatives and real roots of graph polynomials, logic-based computation of graph polynomials, the alliance polynomial, and graph polynomials and set functions.
Historically, this development was not done, as second quantization of the electromagnetic field was first developed.
711 quantizer has been implemented in the first quantization stage and vector quantizer in the second quantization stage.
He covers symmetry groups of elementary particles, the classical theory of free fields and interacting fields, the second quantization of fields, the quantum theory of interacting fields, axiomatic and Euclidean field theories, and the quantum theory of gauge fields.
His topics are the basics of Lagrangian and Hamiltonian mechanics; fundamentals of quantum mechanics; tunneling; problems with a discrete energy spectrum; periodic potentials; the matrix form of quantum mechanics: perturbation theory and density matrix; and spin, identical particle, second quantization, and quantization of the electromagnetic field.
These two candidates are used for replacing the second quantization level, q.
t] via the second quantization vector wave functions of Sound Bosons as
Quantization is a very important part in almost all modern telecommunication systems, and it is usually done in two steps: firstly quantization with high number of levels is done with the aim of the analog-to-digital conversion and after that the second quantization with smaller number of levels is done with the aim of compression.
t) via the second quantization vector wave functions of one Sound Boson of the longitudinal wave.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are, respectively, the second quantization vector wave functions, essentially the vector Bose "creation" and "annihilation" operators for the Bose quasiparticles of electric and magnetic waves with spin one in dielectric medium.
by analogy with the quantum field theory, it can be done the second quantization of the universe wave function [psi] expanding it on the creation and annihilation operators (third quantization) [1].