Quantum corrections during inflation and conservation of adiabatic
  perturbations
  The possibility that quantum corrections break the conservation of
superhorizon adiabatic perturbations in single field inflation is examined. I
consider the lowest order corrections from massless matter fields in the
Hamiltonian formalism. Particular emphasis is therefore laid on the
renormalization. The counterterms are the same as in the Lagrangian formalism.
The renormalized value of the tadpole is zero. I find a possible secular
dependence of the power spectrum at one loop due to the trace anomaly, but this
result depends on the approximation of the modes and is inconclusive. The
symmetry (not) violated by the quantum corrections is the invariance by
dilatation. Perspectives on the backreaction problem are briefly discussed.
