Related papers: The Spectral Shift Function and The Friedel Sum Ru…
Using the spectral theorem we compute the Quantum Fourier Transform (or Vacuum Characteristic Function) $\langle \Phi, e^{itH}\Phi\rangle$ of an observable $H$ defined as a self-adjoint sum of the generators of a finite-dimensional Lie…
Using the Green's function associated with the one-dimensional Schroedinger equation it is possible to establish a hierarchy of sum rules involving the eigenvalues of confining potentials which have only a boundstate spectrum. For some…
Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane wave photons or electrons within the first-order…
A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and…
We use a dispersion relation in conjunction with the operator product expansion (OPE) to derive model independent sum rules for the dynamic structure functions of systems with large scattering lengths. We present an explicit sum rule for…
We present a sum rule relating the electron energy spectrum and the hadron mass distribution in semileptonic b -> u decays close to threshold. The relation found is free from non-perturbative effects and the theoretical error is expected to…
The cross-section for the lowest order $2\rightarrow2$ elastic scattering between two charged scalars under external magnetic field mediated via a neutral scalar, has been computed in strong as well as weak magnetic field limits. This has…
The two photon exchange amplitude is investigated in frame of analytic properties of the virtual Compton scattering amplitude as a function of the invariant mass squared of the intermediate hadronic state. A sum rule is built, based on…
Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of…
We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…
In one-dimensional (1D) non-perturbative many-electron problems such as the 1D Hubbard model the electronic charge and spin degrees of freedom separate into exotic quantum objects. However, there are two different representations for such…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is…
Charge sum rules for quark fragmentation functions are studied. The simultaneous implementation of the conservation of electric and baryon charges, strangeness and isospin symmetry is achieved when the fragmentation to both mesons and…
The main issue in this paper is to discuss a parity property that appears in the expressions for the distorted spectrum of the thermal Sunyaev-Zel'dovich effect. When using the convolution integrals method involving scattering laws we argue…
The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori…
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.
Fluctuation Theorem(FT) has been studied as far from equilibrium theorem, which relates the symmetry of entropy production. To investigate the application of this theorem, especially to biological physics, we consider the FT for tilted…
We use Stirling number identities developed recently in number theory to show that ratios among high energy string scattering amplitudes in the fixed angle regime can be extracted from the Kummer function of the second kind. This result not…
Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of…