Canonical simulations using world-line representations - an exploratory study
In the worldline formulation the particle number of a lattice quantum field theory assumes an elegant topological form: it is the winding number of the worldlines around the compactified time direction. In a numerical worldline simulation one can implement the canonical ensemble by using only updates that preserve the winding number and thus the number of particles. We explore the idea of a canonical simulation in the worldline formulation, using the two-dimensional relativistic Bose gas with a $\phi^4$ self interaction as a model theory. To test the self consistency we study the connection of canonical and grand canonical formulation via summing up the fugacity series and by reconstructing the chemical potential as derivative of the free energy. Finally we discuss how scattering data can be obtained by analyzing the distribution of the worldlines in the canonical ensemble with net particle number 2.