相关论文: Braid Structure and Raising-Lowering Operator Form…
Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured set-up studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how…
The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…
Considering a fluctuating scalar field on momentum space, some relativistic statistical field theories are constructed. A Hilbert space of observables is then constructed from functionals of the fluctuating scalar field with an inner…
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic…
We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting…
In this work we extend the results of [1] where, Semiclassical Selfconsistent Configurations (SSC) formalism was introduced. The scheme combines quantum field theory on a background space-time, semiclassical treatment of gravitation and…
We consider a family of $2 \times 2$ operator matrices ${\mathcal A}_\mu(k),$ $k \in {\Bbb T}^3:=(-\pi, \pi]^3,$ $\mu>0$, acting in the direct sum of zero- and one-particle subspaces of a Fock space. It is associated with the Hamiltonian of…
We propose a deformed version of the commutation rule introduced in 1967 by Buchdahl to describe a particular model of the truncated harmonic oscillator. The rule we consider is defined on a $N$-dimensional Hilbert space $\Hil_N$, and…
We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions,…
We prove dynamical upper bounds for discrete one-dimensional Schroedinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations. We demonstrate the applicability of our approach by a study of…
We consider real scalar field theories whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential $V$. By means of an extension of the standard definition of M{\o}ller operator, we construct an isomorphism…
In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…
In the first half of the paper, we lay down a classical approach to the study of Saito-Kurokawa (SK) lifts of (Hecke congruence) square-free level, including the allied new-oldform theory. Our treatment of this relies on a novel idea of…
We use results from time-frequency analysis and Gabor analysis to construct new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
We reveal a hidden electrodynamical structure emerging from a general $2\times2$ pseudo-Hermitian system that exhibits real spectra. Even when the Hamiltonian does not explicitly depend on time, the Berry curvature can be mapped onto a…
A previously conjectured set of exact form factors of boundary exponential operators in the sinh-Gordon model is tested against numerical results from boundary truncated conformal space approach in boundary sine-Gordon theory, related by…
We have focused in the paper on the most prominent and intensively studied S=1 pseudospin formalism for extended bosonic Hubbard model (EHBM) with truncation of the on-site Hilbert space to the three lowest occupation states n = 0, 1, 2.…
We investigate (pseudo)differential forms in the framework of supergeometry. Definitions, basic properties and Cartan calculus (DeRham differential, Lie derivative, inner product, Hodge operator) are presented; the symplectic supermechanics…