A Relation of the Noncommutative Parameters in Generalized Noncommutative Phase Space

We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space.Based on the deformed boson algebra,we construct coherent state representations.We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations.It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.     

Fock representations and BRST cohomology inSL(2) current algebra

We investigate the structure of the Fock modules overA ₁ ⁽¹⁾ introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of Fock modules. Chiral primary fields are constructed as BRST invariant operators acting on Fock modules. As a result, we obtain a free field representation of correlation functions of theSU(2) WZW model on the plane and on the torus. We also consider representations of fractional level arising in Polyakov's 2D quantum gravity. Finally, we give a geometrical, Borel-Weil-like interpretation of the Wakimoto construction.     

High spin limits and non-abelian T-duality

The action of the non-abelian T-dual of the WZW model is related to an appropriate gauged WZW action via a limiting procedure. We extend this type of equivalence to other σ-models with non-abelian isometries and their non-abelian T-duals, focusing on Principal Chiral models. We reinforce and refine this equivalence by arguing that the non-abelian T-duals are the effective backgrounds describing states of an appropriate parent theory corresponding to divergently large highest weight representations. The proof involves carrying out a subtle limiting procedure in the group representations and relating them to appropriate limits in the corresponding backgrounds. We illustrate the general method by providing several non-trivial examples.     

Infinite-Dimensional Grade Star Representations of the osp (2,l) and spl(2,l) Superalgebras

A grade adjoint operation for the boson and fermion operators is considered. A graded bosonfermion algebra is constructed. Explicit expressions for the generators of the osp(2,l) and spl(2,l) superalgebras in terms of suitable pairs of graded boson and fermion operators are given. Infinite-dimensional grade star representations are obtained.     

Fermions and associated bosons of one-dimensional model

The representation of the canonical commutation relations involved in the construction of boson operators from fermion operators according to the recipe of the neutrino theory of light is studied. Starting from a cyclic Fock-representation for the massless fermions the boson operators are reduced by the spectral projectors of two charge-operators and form an infinite direct sum of cyclic Fock-representations. Kronig's identity expressing the fermion kinetic energy in terms of the boson kinetic energy and the squares of the charge operators is verified as an identity for strictly selfadjoint operators. It provides the key to the solubility ofLuttinger's model. A simple sufficient condition is given for the unitary equivalence of the representations linked by the canonical transformation which diagonalizes the total Hamiltonian.Work supported by the National Science Foundation.     

Fock Representations of Lie Algebras,Loop Algebras and Affine Lie Algebras

Explicit Fock representations of the classical Lie algebras in terms of boson creation and annihilation operators with an arbitrary highest weight are derived, and a general rule to construct Fock represen tations of a loop algebra from a boson realization ofits corresponding Lie algebra is establislted. A new kind of lowest weight represen tations of the affine Lie algebras attached to the classical Lie algebras, which require a zero center, is also presented. Based on these, a simple affinization procedure is given to obtain the Fock representations of level 1 of these affine Lie algebras.     

Boson Realization of Representations for Quantum Groups and Its Differential Correspondence in Bargmann Space

By constructing the q-analogue of the Heisenberg-Weyl algebra in terms of usual creation and annihilation operators of boson states in the Fock space, the boson realization method recently suggested^[7-11] is generalized to obtain a class of representations of quantum group in the Fock space. The q-deformed differential realization of quantum groups proposed by Alvarez-Gaume is derived by making use of the boson realization in this paper.     

Sensitivity study of anomalous HZZ couplings at a future Higgs factory

We study the sensitivity of constraining the model independent HZZ coupling based on the effective theory up to dimension-6 operators at a future Higgs factory. Using the current conceptual design parameters of the Circular Electron Positron Collider, we give the experimental limits for the model independent operators given by the total Higgsstrahlung cross-section and the angular distribution of Z boson decays. In particular, we give the very small sensitivity limit for the CP violation parameter g, which will be a clear window to test the Standard Model and look for new physics signals     

Chiral bosons

The local lagrangian formulation for chiral bosons recently suggested by Floreanini and Jackiw is analyzed. We quantize the system and explain how the unconventional Poincaré generators of left and right chiral bosons combine to form the standard generators. The left-U(1) Kac-Moody algebra and the left-Virasoro algebra are shown to be the same as for left Weyl fermions. We compare the partition functions, on the torus, of a chiral boson and a chiral fermion. The left-moving boson is coupled to gauge fields producing the same anomalies as in the fermionic formulation. It is pointed out that the unconventional Lorentz transformations are inapplicable for the coupled system and a set of different transformations is presented. A coupling to gravity is proposed. We present the theory of chiral bosons on a group manifold, the chiral WZW model. The (1,0) supersymmetric abelian and non-abelian chiral bosons are described.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.     

Various Re-ordering Expressions of General Exponential Quadratic Operators in Mutli-Mode Boson System

In this paper, we give various explicit expressions and transform equalities among usual, normal and anti-normal orderings for the exponential inhomogeneous quadratic (EIQ) operators and their inverse operators in multi-mode boson systems.     

Global Gauge Anomalies in Coset Models of Conformal Field Theory

We study the occurrence of global gauge anomalies in the coset models of two-dimensional conformal field theory that are based on gauged WZW models. A complete classification of the non-anomalous theories for a wide family of gauged rigid adjoint or twisted-adjoint symmetries of WZW models is achieved with the help of Dynkin’s classification of Lie subalgebras of simple Lie algebras.     

On the boson mapping of fermion collective pairs

We study the problem of the mapping of fermion collective pairs onto particle-particle bosons and of different fermion operators (hamiltonian, one- and two-particle transfer operators) onto corresponding boson ones and we test the consequences of the truncation to lowest orders of these boson operators. We find that, although the lowest-order terms in the expansion of the operators in boson space lead to matrix elements between boson states which display the qualitative behaviour of the corresponding ones between fermion states, higher-order terms are required to get a quantitative agreement when a large number of particles are involved, as a direct consequence of the increased role of the Pauli principle.     

On the integrability of representations of finite dimensional real Lie algebras

We give an integrability criterion for Lie algebra representations in a reflexive Banach space. Applications are given to skewsymmetric Lie algebra representations in Hilbert spaces and to essential skewadjointness of a sum of two skewadjoint operators.     

Fusion and braiding in W-algebra extended conformal theories

We define the chiral conformal blocks of integer-spin extended (W-algebra) conformal theories by the fusion of elementary ones. The braid group representation matrices which realize the exchange algebra are computed. They are shown to coincide with the Boltzmann weights — in a certain limit of the spectral parameter — of the critical face models of Jimbo et al. In the unitary cases, where the extended conformal theories can be realized as cosets , we relate the braiding matrices of the former to those of the WZW models. In this article we restrict ourselves to the case corresponding to symmetric tensor representations of A_n.     

A C*-algebra approach to the Schwinger model

If cutoffs are introduced then existing results in the literature show that the Schwinger model is dynamically equivalent to a boson model with quadratic Hamiltonian. However, the process of quantising the Schwinger model destroys local gauge invariance. Gauge invariance is restored by the addition of a counterterm, which may be seen as a finite renormalisation, whereupon the Schwinger model becomes dynamically equivalent to a linear boson gauge theory. This linear model is exactly soluble. We find that different treatments of the supplementary (i.e. Lorentz) condition lead to boson models with rather different properties. We choose one model and construct, from the gauge invariant subalgebra, a class of inequivalent charge sectors. We construct sectors which coincide with those found by Lowenstein and Swieca for the Schwinger model. A reconstruction of the Hilbert space on which the Schwinger model exists is described and fermion operators on this space are defined.     

The orthonormal basis for symmetric irreducible representations of O(5) × SU(1, 1) and its application to the interacting boson model

A main result of the paper is a constructed orthonormal basis for symmetric irreducible representations of the direct group product O(5) × SU(1, 1). Orthonormality is an aim achieved for the first time for this case. The construction was formed from the point of view of its application to the interacting boson approximation in nuclear theory. In this case calculations of matrix elements of physical operators are much simplified because the constructed basis is expressed as linear combinations of the simplest states of the boson harmonic oscillator basis. A couple of examples of such calculations are also demonstrated in the paper.     

Deformed squeezed states in noncommutative phase space

A deformed boson algebra is naturally introduced from studying quantum mechanics on noncommutative phase space in which both positions and momenta are noncommuting each other. Based on this algebra, corresponding intrinsic noncommutative coherent and squeezed state representations are constructed, and variances of single- and two-mode quadrature operators on these states are evaluated. The result indicates that in order to maintain Heisenberg's uncertainty relations, a restriction between the noncommutative parameters is required.