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Well sure, but what's it mean to apply a field with a negative exponent to a field with a positive exponent. Can you treat the operator expansion as inverse matrices? ( I'm still in the habit of expanding fields into c&a operators)
yea the reason we don't know how to treat those is because we never learn .. we never learn them becuase they diverge about 0 or small couplings and hence don't admit a perturbative expansion ..
But you can still yield real eigenvalue s using these types of operators or am I pigeonholing the term observerable too hard.
I honestly don't understand this field all too well .. i understand it when i'm talking to the non perturbative guy here at UCI, but i forget exactly how it's defined non perturbatively
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