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### Field operator eigenstate vs. single-particle state

I would like to make sure I understand some basic QFT. My understanding so far is that field operators measure field intensity and their Fourier transform measure intensity of field oscillation. In ...
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### Eigenvalues of a quantum field

In the book 'Quantum field theory for the Gifted Amateur", the following is stated, cf. 9.3: "A quantum field $\hat{\phi}(x)$ takes a position in spacetime and returns an operator whose eigenvalues ...
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### What are the orthogonal eigenstates of the field operator?

In Peskin & Schroeder section 9.2, they derive the two-point function in the path integral formalism: \langle \Omega | \mathcal{T} \left\{ \hat{\phi}(x_1)\hat{\phi}(x_2)\right\} | \Omega \...
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### Coherent state of second quantized hamiltonian

In my preparation for the exam I tried to solve the exercise 2.4 in Coleman's Introduction to Many-Body Physics. I like diagonalizing Hamiltonian, so I picked this problem. Also to learn more about ...
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### What is the wave field functional?

I was reading on some QFT and I came across the following paragraph: In the same way that a generic state $|\psi\rangle$ of a particle can be described by giving its overlap with all the possible ...
### What is the overlap $\langle \phi | 0 \rangle$ for a scalar field?
Consider a massive free real scalar field $\hat{\Phi}$ (with $\mathcal{L}[\Phi] = \partial_{\mu}\Phi\partial^\mu \Phi - \tfrac{1}{2} m^2 \Phi^2$). I was wondering what is the overlap for the ...
We can construct the unitary transformation for change of basis from $x$ to number operator $n$ in harmonic oscillator by using $a|0\rangle=0$ and then multiply $\langle x|$ to the both side and ...