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In a two-dimensional Bose-Einstein condensate the reduction in dimensionalityfundamentally influences collisions between the atoms. In the crossover regimefrom three to two dimensions several scattering parameters have beenconsidered. However, finite temperature results are more difficult to obtain.In this work we present the many-body T-matrix at finite temperatures within agapless Hartree-Fock-Bogoliubov approach and compare to zero and finitetemperature results obtained using different approaches. A semi-classicalrenormalization method is used to remove the ultra-violet divergence of theanomalous average.Comment: 14 pages, 6 figure

Many-bodyT-matrix of a two-dimensional Bose–Einstein condensate within the Hartree–Fock–Bogoliubov formalism