Related papers: Determinants for the Lightcone Worldsheet
Light-cone perturbation theory is a powerful tool for calculating high-energy scattering amplitudes, particularly for quantum particles such as electrons, photons, or protons scattering off heavy nuclei, a process analogous to potential…
Let X=G/K be a symmetric space of noncompact type and let L be the Laplacian associated with a G-invariant metric on X. We show that the resolvent kernel of L admits a holomorphic extension to a Riemann surface depending on the rank of the…
We numerically investigate the sensitivity of the scattered wave field to perturbations in the shape of a scattering body illuminated by an incident plane wave. This study is motivated by recent work on the inverse problem of reconstructing…
Twist fields were introduced a few decades ago as a quantum counterpart to classical kink configurations and disorder variables in low dimensional field theories. In recent years they received a new incarnation within the framework of…
In this work, we analyze the Dirichlet Laplacian $-\Delta_{\Omega}^D$ in an unbounded waveguide $\Omega \subset \mathbb R^3$, where the cross-section is translated in a constant direction and rotated along a spatial line. We focus on the…
Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic $L^2$ torsion, which lies in the determinant line of the twisted $L^2$ Dolbeault cohomology and represents a volume element there.…
We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical…
The generalization of the conformal scattering method for small-angle scattering processes involving magnetic monopoles and ordinary charges is constructed. Using this generalization we show that introducing of magnetic charges corresponds…
We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degeneration; that is, which converge in a particular way to a…
We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian…
General relativistic imprints on the galaxy bispectrum arise from observational (or projection) effects. The lightcone projection effects include local contributions from Doppler and gravitational potential terms, as well as lensing and…
We show that two-dimensional band insulators, with vanishing bulk polarization, obey bulk-and-edge to corner charge correspondence stating that the knowledge of the bulk and the two corresponding ribbon band structures uniquely determines…
We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in Banach algebras, from a paper by Skandalis and the author…
In this paper, we study the restrictions of both the harmonic functions and the eigenfunctions of the symmetric Laplacian to edges of pre-gaskets contained in the Sierpinski gasket. For a harmonic function, its restriction to any edge is…
We show that tree level ``resonant'' $N$ tachyon scattering amplitudes, which define a sensible ``bulk'' S -- matrix in critical (super) string theory in any dimension, have a simple structure in two dimensional space time, due to partial…
In the AdS/CFT correspondence, wrapped D3-branes (such as "giant gravitons") on the string theory side of the correspondence have been identified with Pfaffian, determinant and subdeterminant operators on the field theory side. We…
In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a…
In this note we describe hadrons: mesons and baryons as strings with electric charges on their endpoints. We consider here only the neutral system with opposite charges coupled to an external constant electric and magnetic fields. We derive…
We implement the worldline formalism in phase space to compute scattering amplitudes. First, the Feynman rules exhibit several useful universal features, reflecting elements of the symplectic geometry of the phase space target. Next,…
In this paper, in continuation of our work, on the determinants of cubic -matrix of order 2 and order 3, we have analyzed the possibilities of developing the concept of determinant of cubic-matrix with three indexes, studying the…