Related papers: Third quantization
Second quantization is an essential topic in senior undergraduate and postgraduate level Quantum Mechanics course. However, it seems that there is a lack of transparent and natural derivation of this formalism from the first-quantization…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
The framework of third quantization - canonical quantization in the Liouville space - is developed for open many-body bosonic systems. We show how to diagonalize the quantum Liouvillean for an arbitrary quadratic n-boson Hamiltonian with…
The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
In [1] a new bosonization procedure has been illustrated, which allows to express a fermionic gaussian system in terms of commuting variables at the price of introducing an extra dimension. The Fermi-Bose duality principle established in…
In this paper we provide a novel and general way to construct the result of the action of any bosonic or fermionic operator represented in second quantized form on a state vector, without resorting to the matrix representation of operators…
We derive several formulae for the spectra of the second quantization operators in abstract fermionic Fock spaces.
We develop a bosonization procedure on the half line. Different boundary conditions, formulated in terms of the vector and axial fermion currents, are implemented by using in general the mixed boundary condition on the bosonic field. The…
This is a self-contained and hopefully readable account on the method of creation and annihilation operators (also known as the Fock space representation or the "second quantization" formalism) for non-relativistic quantum mechanics of many…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which $\hbar >0$ throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action…
One of the traditional ways of introducing bosons and fermions is through creation-annihilation algebras. Historically, these have been associated with emission and absorption processes at the quantum level and are characteristic of the…
By application of the general twist-induced star-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime in a non-commutative language. The procedure deforms in a coordinated way the…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…
It is shown that some analog of the ``second quantization'' exists in the framework of CP(N) theory. I analyse conditions under that ``geometrical bosons'' may be identified with real physical fields. The compact character of a state…
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…