Old Fashioned Perturbation Theory
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چکیده
We will spend only a short time reviewing old fashioned perturbation theory and exploring its application in quantum field theory. The essentials in QFT are the same as they were in non-relativitstic quantum mechanics, where we split the Hamiltonian into two parts a “free" solvable Hamiltonian, H0 and an interacting part Hint 42 This separation is often troublesome, as symmetries may relate operators in H0 with operators in Hint. This is the case in gauge theories. Perturbation theory then breaks apart certain amplitudes, with symmetry manifest only after all contributions are summed at a given order in the perturbative expansion. (where the interactions are small in some sense, relative to the interactions). We can then write the full Hamiltonian as
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