Quasi-particles at finite temperatures
In analogy to scattering theory of quantum fields we construct quasiparticles with the help of spectral properties of the Hamiltonian and time limits. We assume that in the joint spectral representation of time and space translation operators there is a \(\delta\)-type singularity for some dispersion relation. Assuming furthermore cluster properties or sufficiently strong asymptotic abelianness we construct creation and annihilation operators as the operators, that map the GNS vector \(\Omega\) onto the subspace corresponding to the \(\delta\)-type singularity. These operators are unique, in contrast to quantum field theory. They correspond to fermions or bosons, depending on the kind of cluster properties resp. commutation relations.
joint spectral representation of time and space translation operators
scientific article; zbMATH DE number 3848043
scientific article