Relativistic Levinson theorem in two dimensions

Generalized Levinson theorem for singular potentials in two dimensions

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states Nm b in a given mth partial wave is related to the phase shift dm(k) and the singularity strength of the potential. When the effective potential has an inverse square singularity at the origin of the form n/r and inverse square tail at ...

Levinson theorem for Aharonov-Bohm scattering in two dimensions

In 1949 Levinson 1 established one of the most beautiful results of scattering theory: the Levinson theorem sets up a relation between the number of bound states, Nl , in a given lth partial wave and the phase shift l k : namely, l 0 − l = Nl . Ten years later, in 1959, Aharonov and Bohm 2 discovered the global properties of the magnetic flux. Nowadays the Aharonov-Bohm AB effect is often invol...

Relativistic quantum thermodynamics of ideal gases in two dimensions.

In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.

A Relativistic Polaron without Cutoffs in Two Space Dimensions

Cluster simulation of relativistic fermions in two space-time dimensions

For Majorana-Wilson lattice fermions in two dimensions we derive a dimer representation. This is equivalent to Gattringer’s loop representation, but is made exact here on the torus. A subsequent dual mapping leads to yet another representation in which a highly efficient Swendsen-Wang type cluster algorithm is constructed. It includes the possibility of fluctuating boundary conditions. It also ...