Boson-Fermion Fock Space Research Articles

Parabosons, parafermions and representations of ℤ2 × ℤ2-graded Lie superalgebras

For a set of m parafermion operators and n paraboson operators, there are two nontrivial ways to unify them in a larger algebraic structure. One of these corresponds to the orthosymplectic Lie superalgebra . The other one is no longer a ℤ2-graded Lie superalgebra but a ℤ2 × ℤ2-graded Lie superalgebra, a rather different algebraic structure, denoted here by . In a recent paper, the Fock spaces of order p for were determined. In the current paper, we summarize some of the main properties of and its Fock spaces. In particular, we concentrate on the Fock space for p = 1, and indicate how it reduces to an ordinary boson-fermion Fock space.

Z 2 × Z 2 generalizations of N=1 superconformal Galilei algebras and their representations

We introduce two classes of novel color superalgebras of Z2×Z2 grading. This is done by realizing members of each class within the universal enveloping algebra of the N=1 supersymmetric extension of the conformal Galilei algebra. This allows us to upgrade any representation of the super conformal Galilei algebras to a representation of the Z2×Z2 graded algebra. As an example, boson-fermion Fock space representation of one class is given. We also provide a vector field realization of members of the other class by using a generalization of the Grassmann calculus to Z2×Z2 graded setting.

Ground states of quantum electrodynamics with cutoffs

In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is a self-adjoint operator on a boson-fermion Fock space. It is shown that under spatially localized conditions and momentum regularity conditions, the total Hamiltonian has a ground state for all values of coupling constants. In particular, its multiplicity is finite.

ITÔ–WIENER CHAOS AND THE HODGE DECOMPOSITION ON AN ABSTRACT WIENER SPACE

Using the structure of the Boson-Fermion Fock space and an argument taken from [P. Bieliavsky, M. Cahen, S. Gutt, J. Rawnsley and L. Schwachhofer, Symplectic connections, Int. J. Geom. Meth. Mod. Phys.3 (2006) 375–420], we give a new proof of the triviality of the L2 cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [De Rham–Hodge–Kodaira's decomposition on an abstract Wiener space, J. Math. Kyoto. Univ.26(2) (1986) 191–202]. We apply the representation theory of the symmetric group to characterize the spaces of exact and co-exact forms in their Boson-Fermion Fock space representation.

GROUND STATE OF THE YUKAWA MODEL WITH CUTOFFS

The ground state of the Yukawa model is considered. The Yukawa model describes the system of a Dirac field interacting with a Klein–Gordon field. By introducing ultraviolet cutoffs and spatial cutoffs, the total Hamiltonian is defined as a self-adjoint operator on a boson–fermion Fock space. It is shown that the total Hamiltonian has a positive spectral gap for all values of coupling constants. In particular, the existence of the ground state is proven.

Infinite-Dimensional Analysis and Analytic Number Theory

We consider arithmetical aspects of analysis on Fock spaces (Boson Fock space, Fermion Fock space, and Boson–Fermion Fock space) with applications to analytic number theory.

Strong anticommutativity of dirac operators on boson—fermion fock spaces and representations of a supersymmetry algebra

AbstractOn the boson—fermion Fock space F(H, K) associated with two complex Hilbert spaces H and K, there exists a family {Qs | S ∈ C(H, K)} of Dirac type operators, where C(H, K) is the set of densely defined closed linear operators from H to K. A theorem on the strong anticommutativity of two Dirac operators QS and QT is established. As an application, representations on F(H, K) of a supersymmetry algebra arising in a two—dimensional relativistic supersymmetric quantum field theory are discussed.

On self-adjointness of Dirac operators in Boson-Fermion Fock spaces

It is shown that a class of Dirac operators acting in the abstract Boson-Fermion Fock space, which were introduced in a previous paper (A. Arai, J. Funct. Anal. 105 (1992), 342-408), is essentially self-adjoint. The result is applied to the Wess-Zumino models of supersymmetric quantum field theory to prove the essential self-adjointness of their supercharges and Hamiltonians.

Dirac operators in Boson-Fermion Fock spaces and supersymmetric quantum field theory

Infinite dimensional analysis is developed on an abstract Boson-Fermion Fock space. A general class of Dirac operators acting there is introduced and properties of them are investigated. An index theorem for the Dirac operators is established in terms of a path integral on a loop space. It is shown that the abstract formalism presented here gives a mathematical unification for some models of supersymmetric quantum field theory.