Momentum space renormalisation of λϕ4in curved space-time

As an extension of previous work which developed a method for performing calculations in curved space-time quantum field theory using momentum space, it is shown how the technique can be used to great advantage in the computation of both the divergent and finite parts of S-matrix elements for self-interacting lambda phi 4 theory. Using dimensional regularisation all the pole terms in the self-energy up to second order are calculated, to confirm that, to this order, mass-independent renormalisation can be successfully applied.