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The usual formulation of quantum field theory in Minkowski
spacetime relies heavily on Poincare invariance and the existence of a
Poincare invariant vacuum state. Standard renormalization prescriptions in
Minkowski spacetime rely heavily on techniques such as momentum space
methods and Euclideanization. None of these features have a
straightforward generalization to curved Lorentzian spacetimes.
Nevertheless, during the past ten years, a mathematically rigorous
perturbative formulation of interacting quantum field theory in curved
spacetime has been given. I will summarize this progress and describe the
nature of the resulting theory, where, at a fundamental level, there is no
preferred "vacuum state" or preferred notion of "particles" and where
"vacuum subtraction" is clearly seen to be an incorrect renormalization
prescription (except in Minkowski spacetime).
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