The subject of this thesis is the modular group of automorphisms acting on
the massive algebra of local observables having their support in bounded open
subsets of Minkowski space. After a compact introduction to micro-local
analysis and the theory of one-parameter groups of automorphisms, which are
used exensively throughout the investigation, we are concerned with modular
theory and its consequences in mathematics, e.g., Connes' cocycle theorem and
classification of type III factors and Jones' index theory, as well as in
physics, e.g., the determination of local von Neumann algebras to be
hyperfinite factors of type III_1, the formulation of thermodynamic equilibrium
states for infinite-dimensional quantum systems (KMS states) and the discovery
of modular action as geometric transformations. However, our main focus are its
applications in physics, in particular the modular action as Lorentz boosts on
the Rindler wedge, as dilations on the forward light cone and as conformal
mappings on the double cone. Subsequently, their most important implications in
local quantum physics are discussed.
The purpose of this thesis is to shed more light on the transition from the
known massless modular action to the wanted massive one in the case of double
cones. First of all the infinitesimal generator of the massive modular group is
investigated, especially some assumptions on its structure are verified
explicitly for the first time for two concrete examples. Then, two strategies
for the calculation of group itself are discussed. Some formalisms and results
from operator theory and the method of second quantisation used in this thesis
are made available in the appendix
