Related papers: Function Theory on a q-Analog of Complex Hyperboli…
In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are…
In this paper we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional…
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. The paper gives a systematic method for computing the…
A new formalism is introduced to treat problems in quantum field theory, using coherent functional expansions rather than path integrals. The basic results and identities of this approach are developed. In the case of a Bose gas with…
We introduce a $q$-deformation of the Fock space of holomorphic functions on $\mathbb{C}$, based on a geometric definition of $q$-analyticity. This definition is inspired by a standard construction in complex differential geometry. Within…
The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Fock representations are constructed for a free scalar field in the closed and quasi-Euclidean isotropic cosmological models. Invariance of their cyclic vector (vacuum) under isometries and the correspondence principle single out a class of…
We find kernel functions of the $q$-Heun equation and its variants. We apply them to obtain $q$-integral transformations of solutions to the $q$-Heun equation and its variants. We discuss special solutions of the $q$-Heun equation from the…
We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr's holomorphic almost periodic functions on tube domains or algebras of all…
We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
The theory of $q$-analogs frequently occurs in a number of areas, including the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play a prominent role in the study of $q$-deformed quantum mechanical simple harmonic…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…
In this survey paper, we will collate various different ideas and thoughts regarding equivariant operations on quantum cohomology (and some in more general Floer theory) for a symplectic manifold. We will discuss a general notion of…
We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted…
We study several integrable Hamiltonian systems on the moduli spaces of meromorphic functions on Riemann surfaces (the Riemann sphere, a cylinder and a torus). The action-angle variables and the separated variables (in Sklyanin's sense) are…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…