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eoghan

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- Why are the commutation relations for interacting fields assumed to be the same as that of free fields?

Hi there,

In his book "Quantum field theory and the standard model", Schwartz assumes that the canonical commutation relations for a free scalar field also apply to interacting fields (page 79, section 7.1). As a justification he states:

I do not understand this explanation. Can you please elaborate?

I mean, how can the Hilbert space of the interacting theory be the same as the one of the free theory? In an interacting theory, I expect to have different states than in a non interacting theory, so the Hilbert space should be different, isn't it?

In his book "Quantum field theory and the standard model", Schwartz assumes that the canonical commutation relations for a free scalar field also apply to interacting fields (page 79, section 7.1). As a justification he states:

This is a natural assumption, since at any given time the Hilbert space for the interacting theory is the same as that of a free theory.

I do not understand this explanation. Can you please elaborate?

I mean, how can the Hilbert space of the interacting theory be the same as the one of the free theory? In an interacting theory, I expect to have different states than in a non interacting theory, so the Hilbert space should be different, isn't it?