Related papers: Hilbert space theory for relativistic dynamics wit…
We consider reflection-positivity (Osterwalder-Schrader positivity, O.S.-p.) as it is used in the study of renormalization questions in physics. In concrete cases, this refers to specific Hilbert spaces that arise before and after the…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
Let K be a compact Lie group, endowed with a bi-invariant Riemannian metric. The complexification G of K inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and left and right translation turn the…
Recently, 't Hooft's S-matrix for black hole evaporation, obtained from the gravitational interactions between the in-falling particles and Hawking radiation, has been generalised to include transverse effects. The action describing the…
The analyticity properties of the scattering amplitude for a massive scalar field is reviewed in this article where the spacetime geometry is $R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigated the analyticity of…
We introduce a class of particle models in one dimension involving exchange interactions that have scattering properties satisfying the Yang-Baxter consistency condition. A subclass of these models exhibits reflectionless scattering, in…
In this paper, we consider natural Hilbert-space representations $\left\{ \left(\mathbb{C}^{2},\pi_{t}\right)\right\} _{t\in\mathbb{R}}$ of the hypercomplex system $\left\{ \mathbb{H}_{t}\right\} _{t\in\mathbb{R}}$, and study the…
A problem of monoenergetic particles pulse reflection from half-infinite stratified medium is considered in conditions of elastic scattering with absorbtion account. The theory is based on multiple scattering series solution of Kolmogorov…
We argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in…
A class of integral transforms, on the planar Gaussian Hilbert space with range in the weighted Bergman space on the bi-disk, is defined as the dual transforms of the 2d fractional Fourier transform associated with the Mehler function for…
We construct a class of representations of the quadratic $R$-matrix algebra given by the reflection equation with the spectral parameter, $$ R{\,}(u-v)\,T^{(1)}(u)\,R{\,}(u+v)\,T^{(2)}(v)= T^{(2)}(v)\,R{\,}(u+v)\,T^{(1)}(u)\,R{\,}(u-v), $$…
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable,…
We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order…
We present here an efficient method which systematically reduces the rank of the augmented space and thereby helps to implement augmented space recursion for any real calculation. Our method is based on the symmetry of the Hamiltonian in…
We explore certain properties of the Hartree-Fock approximation to the ground state of the two-dimensional Hubbard model, emphasizing the fact that in the Hartree approach there is an enormous multiplicity of self-consistent solutions which…
Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming…
It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…
We study two simple real analytic uniformly hyperbolic dynamical systems: expanding maps on the circle S1 and hyperbolic maps on the torus T2. We show that the Ruelle-Pollicott resonances which describe time correlation functions of the…
Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span $L_X^2$ of $X$. This paper investigates…
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…