On the pointwise convergence of the integral kernels in the Feynman-Trotter formula [PDF]
, 2019 We study path integrals in the Trotter-type form for the Schr\"odinger equation, where the Hamiltonian is the Weyl quantization of a real-valued quadratic form perturbed by a potential $V$ in a class encompassing that - considered by Albeverio and It\^o ...
Nicola, Fabio, Trapasso, S. Ivan
core +2 more sources
Alternative sets of hyperspherical harmonics: Satisfying cusp conditions through frame transformations [PDF]
, 1999 By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics.
Dmitry Green +2 more
core +3 more sources
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons [PDF]
, 2010 In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\
F. Bagarello +3 more
core +5 more sources
Ghost-Free de Sitter Supergravities as Consistent Reductions of String and M-theory [PDF]
, 2004 We study properties of supergravity theories with non-compact gaugings, and their higher-dimensional interpretations via consistent reductions on the inhomogeneous non-compact hyperboloidal spaces {\cal H}^{p,q}.
Behrndt +29 more
core +3 more sources
Geometric renormalization of large energy wave maps [PDF]
, 2004 There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization ...
Tao, Terence
core +4 more sources
New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology [PDF]
, 2006 We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative
A. Manning +12 more
core +5 more sources
A non-linear Oscillator with quasi-Harmonic behaviour: two- and $n$-dimensional Oscillators
, 2004 A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the classical and also at ...
Ballesteros A +33 more
core +1 more source
Metric duality between positive definite kernels and boundary processes
, 2017 We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes.
Jorgensen, Palle, Tian, Feng
core +1 more source
A short proof of commutator estimates [PDF]
, 2018 The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools.
D'Ancona, Piero
core +2 more sources
Testing extra dimensions with boundaries using Newton's law modifications
, 2011 Extra dimensions with boundaries are often used in the literature, to provide phenomenological models that mimic the standard model. In this context, we explore possible modifications to Newton's law due to the existence of an extra-dimensional space, at
Abramowitz M. +7 more
core +1 more source