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I'm not quite following why Wick's Theorem only applies to free fields. What part of the argument depends on a free field assumption?
Wick's Theorem for free fields only is a mathematical tool used in quantum field theory to simplify the calculation of correlation functions of free fields. It states that the expectation value of a product of field operators can be expressed as a sum of products of the expectation values of individual field operators.
Wick's Theorem for free fields only can be derived from the commutation relations of the field operators and the definition of the normal ordering of operators. It is essentially a consequence of the linearity and locality properties of quantum field theory.
Wick's Theorem for free fields only assumes that the fields are free, meaning they do not interact with each other. It also assumes that the fields are bosonic or fermionic fields, and that they are in their ground state.
No, Wick's Theorem for free fields only cannot be applied to interacting fields because it assumes that the fields are free and do not interact with each other. However, there are extensions of Wick's Theorem that can be applied to certain types of interacting fields.
Wick's Theorem for free fields only simplifies the calculation of correlation functions of free fields by breaking them down into products of simpler expectation values. This allows for easier and more efficient calculations in quantum field theory.