26,228 research outputs found
Numerical integrators for motion under a strong constraining force
This paper deals with the numerical integration of Hamiltonian systems in
which a stiff anharmonic potential causes highly oscillatory solution behavior
with solution-dependent frequencies. The impulse method, which uses micro- and
macro-steps for the integration of fast and slow parts, respectively, does not
work satisfactorily on such problems. Here it is shown that variants of the
impulse method with suitable projection preserve the actions as adiabatic
invariants and yield accurate approximations, with macro-stepsizes that are not
restricted by the stiffness parameter
Electromagnetic Potential in Pre-Metric Electrodynamics: Causal Structure, Propagators and Quantization
An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics
is just one instance of a variety of theories for which the name
electrodynamics is justified. They all have in common that their fundamental
input are Maxwell's equations (or ) and
and a constitutive law H = # F which relates the field
strength two-form and the excitation two-form . A local and linear
constitutive law defines what is called local and linear pre-metric
electrodynamics whose best known application are the effective description of
electrodynamics inside media including, e.g., birefringence. We analyze the
classical theory of the electromagnetic potential before we use methods
familiar from mathematical quantum field theory in curved spacetimes to
quantize it in a locally covariant way. Our analysis of the classical theory
contains the derivation of retarded and advanced propagators, the analysis of
the causal structure on the basis of the constitutive law (instead of a metric)
and a discussion of the classical phase space. This classical analysis sets the
stage for the construction of the quantum field algebra and quantum states.
Here one sees, among other things, that a microlocal spectrum condition can be
formulated in this more general setting.Comment: 34 pages, references added, update to published version, title
updated to published versio
Invariant meromorphic functions on Stein spaces
In this paper we develop fundamental tools and methods to study meromorphic
functions in an equivariant setup. As our main result we construct quotients of
Rosenlicht-type for Stein spaces acted upon holomorphically by
complex-reductive Lie groups and their algebraic subgroups. In particular, we
show that in this setup invariant meromorphic functions separate orbits in
general position. Applications to almost homogeneous spaces and principal orbit
types are given. Furthermore, we use the main result to investigate the
relation between holomorphic and meromorphic invariants for reductive group
actions. As one important step in our proof we obtain a weak equivariant
analogue of Narasimhan's embedding theorem for Stein spaces.Comment: 20 pages, 1 figur
- …