A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A duality between Schrödinger operators on graphs and certain Jacobi matrices
A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum.
A field equation defined by a Hurwitz pair
A functorial approach to differential characters.
A fundamental geometry of quantum physics.
A gauge theoretical approach to space-time structures
A gauge-field approach to 3- and 4-manifold invariants
An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.
A generalised Hopf algebra for solitons.
A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators.
A generalization of the conservation integral
Starting from the scheme given by Hudson and Parthasarathy [7,11] we extend the conservation integral to the case where the underlying operator does not commute with the time observable. It turns out that there exist two extensions, a left and a right conservation integral. Moreover, Itô's formula demands for a third integral with two integrators. Only the left integral shows similar continuity properties to that derived in [11] used for extending the integral to more than simple integrands. In...
A generalization of the radiation condition of Sommerfeld for -body Schrödinger operators
A generalized coherent state approach of the quantum dynamics for suitable time-dependent hamiltonians
A generating function for fatgraphs
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
A geometrical interpretation of the time evolution of the Schrödinger equation for discrete quantum systems
A journey between two curves.
A Lie algebroid on the Wiener space.
A Lieb-Thirring bound for a magnetic Pauli Hamiltonian (II).
We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
A low temperature expansion for the pseudoscalar Yukawa model of quantum fields in two space-time dimensions