A numerical study of scattering processes in Euclidean quantum field theories

Who: Christian Walther Andersen (CP3-Origins)
When: Friday, August 19, 2016

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In this thesis we study how scattering phase shifts of a quantum field theory can be measured on the lattice. We review the theory of Markov processes related to updating algorithms as well as autocorrelation and error estimation before moving on to the model of interest, the O(3) non-linear sigma-model. To simulate the model we use the Cluster algorithm which is described in detail and tested on the Ising model along with other algorithms for comparison. We find that the Cluster algorithm outperforms the local updating algorithms when both accuracy and time are taken into account. We proceed to study the tools necessary to approach the continuum limit and use results from the literature to improve the lattice we are using. We then show how to compute the mass of the particles in the model, as well as the scattering phase shifts using the finite volume energy spectrum of the two-particle states. It is shown how the problem of calculating the energy of a two particle scattering state is essentially a generalised eigenvalue problem with matrices constructed from four point correlation functions. For the mass we see clear scaling violations of order a^2 from which we compute the expected continuum mass of the model. The measurements of the scattering phase shifts similarly showed that for the coarse lattices there are deviations from the known analytical solution, which seems to disappear when going to lattices with smaller spacing.