arXiv subjects
Publications and source records attributed to H. Kröger.
We suggest as gedanken experiment a generalization of the Aharonov-Bohm experiment, based on an array of solenoids. This experiment allows in principle to measure the decomposition into homotopy classes of the quantum mechanical propagator. This yields information on the geometry of the average path of propagation and allows to determine its Hausdorff dimension.
We study the geometry of propagation of relativistic fermions. We propose how to measure its quantum mechanical length. Numerical lattice results for the free propagator of Dirac-Wilson fermions yield Hausdorff dimension d_H=2 for the unit-matrix component and d_H=1 for any gamma-matrix component. A possible generalization when matter interacts with radiation is discussed.
We consider a fractal Wilson loop $ $ and present physical arguments why this should be a relevant observable in nature. We show for non-compact SU(2) lattice gauge theory in the next to leading order of strong coupling expansion that $ $ obeys an area law behavior and is gauge invariant.
We study glueball and meson scattering in compact $QED_{2+1}$ gauge theory in a Hamiltonian formulation and on a momentum lattice. We compute ground state energy and mass, and introduce a compact lattice momentum operator for the computation of dispersion relations. Using a non-perturbative time-dependent method we compute scattering cross sections for glueballs and mesons. We compare our results with strong coupling perturbation theory.
We have studied the scalar $ϕ^4$-model in the symmetric phase and the non--compact $U(1)$ gauge theory on a momentum lattice using the Langevin equation for generating configurations. In the $ϕ^4$-model we have analyzed the renormalized mass and in the $U(1)$-model we have analyzed the Wilson loop operator. We used a second order algorithm for solving the Langevin equation, and we looked for the convergence rate of the method. We studied the stochastic time needed to generate equilibrium configurations and compared first and second order schemes for both models.
The evolution equation for the expectation values of the Boltzmann factor between valence bond states is evaluated in lowest order of the dimer cluster expansion. Explicit formulas are given for the internal energy and the specific heat of the d-dimensional antiferromagnetic Heisenberg model.