I am having some great difficulty getting intuition out of the standard quantization of the Klein-Gordon Lagrangian.(adsbygoogle = window.adsbygoogle || []).push({});

consider the H operator. In QM, the expectation values for H in any eigenstates |n> is just

<n|H|n>

now, in QFT, suppose I have a state |p> in the universe, what do I get if I measure the energy?

well, simply the eigenvalues under H, so E_p. But if I go ahead and try:

<p|H|p>, i get [tex]\delta (0) E_p (2\pi)^3 (2E_p)[/tex]

so, how should I make sense of <p|H|p> ?

in general, suppose I have an operator, Q, corresponding to a measurement of some observables, how do I find the expectation values? specially when the states are not eigenstates of Q?

One more question, what does the state

[tex]\left|\psi \right> =a\left| 0 \right> + b\left | p \right>[/tex] mean? and how should it be normalized?

i.e. [tex]\left< \psi \left| \psi \right>[/tex] should be what?

Also, In the usual QM, we can roughly think of psi as a state who's probability of being in 0 is |a|^2 and probability of being in p is |b|^2. However, that is completely based on the fact that <0|0> = <p|p>=1, <0|p>=0. in QFT, <p|p> gives delta function at zero, so how to interpret psi?

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# How to get QFT operator expectation values?

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