0
$\begingroup$

In many QFTs we can define a stress tensor $T^{\mu\nu}$. What is the matrix element of $T^{\mu\nu}$ in momentum eigenstates? For instance, consider

$$\langle q | T^{\mu\nu} |q\rangle$$

in QCD, where $|q\rangle$ is a proton with momentum $q$. (According to Schwartz Eq. 32.106, this is $= q^{\mu}q^{\nu}$--- but why?).

One thing we may note is $\int d^3x\, T^{0\nu} = P^{\nu}$, so $\int d^3x\, \langle q | T^{0\nu} |q\rangle = q^{\nu} \langle q | q\rangle$; but in general I do not know how to find $\langle q | T^{\mu\nu} |q\rangle$.

$\endgroup$
  • 1
    $\begingroup$ The stress-energy tensor is an operator given in terms of the field operator and its derivatives. Do you know how to find the expectation value of the field operator and/or its derivatives? $\endgroup$ – Void Jan 25 at 16:56
  • $\begingroup$ @Void I suppose I could try to find $T^{\mu\nu}$ explicitly, plug in the creation/annihilation operator expansions and try to find the answer that way. But I was wondering if there is a general expression (such as what Schwartz posits, $\langle q | T^{\mu\nu} |q \rangle = q^{\mu}q^{\nu}$) in QFT which is independent of whatever crazy form $T^{\mu\nu}$ or the fields may take-- even if it's not completely general and requires a few assumptions. $\endgroup$ – Dwagg Jan 25 at 22:01

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.