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I came across this in the lecture notes of quantum field theory by David Tong. Inside time ordering interactions aren’t taken to be normal ordered. Interaction hamiltonian should be normal ordered otherwise it is not well defined (due to ordering ambiguity and related singularities). Most standard QFT textbooks don’t address this issue. Am i missing something here or normal ordering was assumed?

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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/133426/2451 , physics.stackexchange.com/q/10804/2451 and links therein. $\endgroup$ – Qmechanic Nov 1 '20 at 22:02
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    $\begingroup$ This doesn’t answer my question. My question is whether we use normal ordered hamiltonian in s matrix or not and why books don’t take normal ordered hamiltonian? I am confused about this point. $\endgroup$ – Roy Nov 2 '20 at 2:15
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    $\begingroup$ Schwarz’s and peskin’s book don’t mention this issue. So am i right or wrong? $\endgroup$ – Roy Nov 2 '20 at 2:34
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    $\begingroup$ Also Joe Polchinski in his string theory book says normal ordering is of little use in most interacting field theories , because these have additional divergences from interaction vertices approaching the composite operator or one another. Again i am confused because without normal ordering these composite operators aren’t well defined. $\endgroup$ – Roy Nov 2 '20 at 2:50
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    $\begingroup$ normal ordering can be undone by an appropriate choice of counterterms. since normal ordering does not remove all divergences in interacting field theories one needs further counterterms. so one can instead work with a different set of counterterms from the outset, one that removes all divergences from the outset with no reference to normal ordering. there is a normal ordering that is useful also in interacting theories (google: complete normal ordering), which serves to ensure you land on the quantum corrected vacuum, but here too there are further divergences and more counterterms are needed $\endgroup$ – Wakabaloola Nov 2 '20 at 5:34
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Here there should be normal ordering for individual interaction terms inside time ordering.

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