The Hamiltonian Formalism in Quantum Field Theory

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In quantum field theory, we very often imagine that we're in a euclidean metric space time. We do calculations there and then say, ok, that implies a certain answer back in the real world. So you can definitely imagine physics working in that kind of construction. There would still be ways to do physics if all directions of space time were space like rather than time like but you probably wouldn't use hamiltonian formalism for doing it.

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