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A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with…
We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson…
Since the basic theoretical framework of generalized Hamilton system is not perfect and complete, there are often some practical problems that can not be expressed by generalized Hamilton system. The generalized gradient operator is defined…
Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons. We first establish that translational symmetry, together with a fixed pair interaction,…
We open a new discussion of generalized canonical partition function in standard statistical mechanics and apply it for the study of Bose-Einstein condensation. We discuss the possible cases for the generalized canonical partition function…
We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…
We study generalized gauge theories engineered by taking the low energy limit of the $Dp$ branes wrapping $X \times T^{p-3}$, with $X$ a possibly singular surface in a Calabi-Yau fourfold $Z$. For toric $Z$ and $X$ the partition function…
We study the description of single-species and isovector pairing correlations in the framework of the projected-BCS (PBCS) and the Quartet Condensation Model (QCM) from a particle-hole perspective and we introduce the representation of the…
In this paper we deal with the generalized Gamma processes and their compositions. For the compositions of two or more than two generalized Gamma processes we give, when possible, the explicit law whereas, in the other cases the…
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…
We investigate a generalization of $A_r$ statistics discussed recently in the literature. The explicit complete set of state vectors for the $A_r$ statistics system is given. We consider a Bargmann or an analytic function description of the…
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches.…
We present relations between Hirota-type bilinear operators, scalar products on spaces of symmetric functions and integrals defining matrix model partition functions. Using the fermionic Fock space representation, a proof of the expansion…
The Macdonald process is a stochastic process on the collection of partitions that is a $(q,t)$-deformed generalization of the Schur process. In this paper, we approach the Macdonald process identifying the space of symmetric functions with…
We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit…
We construct a representation of $U_q(\widehat{sl}_2)$ at level $-1/2$ by using the bosonic Fock spaces. The irreducible modules are obtained as the kernel of a certain operator, in contrast to the construction by Feingold and Frenkel for…
We consider the fermion mass renormalization due to the vector boson exchange within mesodynamics with nucleon and $\rho$ meson fields as well as quantum electrodynamics with electron and photon fields. The method of unitary clothing…
The standard-model can be equivalently represented with its fields in a spin-extended basis, departing from fermion degrees of freedom. The common Higgs operator connects the electroweak and Yukawa sectors, restricting the top and bottom…
The reduced k-particle density matrix of a density matrix on finite-dimensional, fermion Fock space can be defined as the image under the orthogonal projection in the Hilbert-Schmidt geometry onto the space of k-body observables. A proper…
A combinatorial study of multiple $q$-integrals is developed. This includes a $q$-volume of a convex polytope, which depends upon the order of $q$-integration. A multiple $q$-integral over an order polytope of a poset is interpreted as a…