All Questions
24
questions
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About momentum states covariant normalization
I'm following QFT of Schwrtz and I have a doubt about Eq. (2.72).
In particular, from Eq. (2.69): $$[a_k,a_p^\dagger]=(2\pi)^3\delta^3(\vec{p}-\vec{k}),\tag{2.69}$$ and Eq. (2.70): $$a_p^\dagger|0\...
- 147
3
votes
1
answer
176
views
How to normalize the states in the continuous limit?
In quantum field theories we can perform the continuous limit, where we take the limit $V\rightarrow\infty$ for the volume system. In quantum optics, we can start by absorbing a factor $\left(\frac{L}{...
- 865
2
votes
1
answer
66
views
Why two energies look same in the relativistic normalization?
I'm reading Peskin's QFT textbook.
In this book, to make normalization of momentum eigenstate Lorentz invariant, we define momentum eigenket as
$$\left| \mathbf{p} \right> = \sqrt{2E_{\mathbf{p}}} ...
- 47
2
votes
0
answers
103
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(Srednicki) How to obtain the normalization condition for Dirac field?
I'm reading through srednicki's qft and I met a problem. In its section 41, after he make an assumption that the creation operators of free field
theory would work comparably in the interacting theory ...
- 125
3
votes
1
answer
507
views
Why do we need to normalise states in quantum field theory?
In QM its obvious that we need to normalise quantum states since their inner product squared represents a probability. This normalization leads to physical states in QM being represented by 'rays' of ...
- 2,604
4
votes
0
answers
667
views
Normalization of One-Particle States for Klein-Gordon Field Quantization
Peskin & Schroeder in their QFT textbook discusses how we may normalize one-particle states $|\textbf{p}\rangle$ for Klein-Gordon field quantization in pages 22-23. The excerpts are given below.
...
- 3,023
5
votes
0
answers
243
views
LSZ formula in Srednicki, normalization issue
In the Ch.5 of his book, Srednicki says LSZ formula is valid provided the following conditions hold:
$$
\langle 0|\phi(x)|0\rangle = 0, \langle p|\phi(x)|0\rangle = 1
$$
To achieve these conditions, ...
- 51
1
vote
0
answers
112
views
Weinberg's normalization convention for momentum eigenstates
In this answer https://physics.stackexchange.com/a/376193/274751 two different conventions for the normalization of momentum eigenstates are mentioned.
This convention amounts to the choice of $N(p)$ ...
7
votes
2
answers
661
views
Normalization of vacuum state in field theory
I am doing a calculation of an amplitude in QFT, not an expert in the subject so this may be a trivial question but cannot find the answer.
What is the normalization of the vacuum state of the ...
- 1,872
4
votes
1
answer
572
views
Normalization of momentum eigenstates in QFT
Inspired by a previous question, I'd like to ask about the normalization of one-particle states in QFT.
The most common normalization seems to be the covariant one:
$$ \langle \vec p'|\vec p\rangle = (...
- 2,648
0
votes
1
answer
181
views
How the normalization condition implies the following relation?
Using equation 2.35 from Peskin and Schroeder:
$$
|\vec{p}\rangle=\sqrt{2 E_{\vec{p}}} a^{\dagger}_\vec{p} |0\rangle
$$
should lead to
$$
U(\Lambda)|\vec{p}\rangle = |\Lambda \vec{p}\rangle,
$$
where ...
- 297
2
votes
1
answer
195
views
How to compute normalization of one-particle states for Klein-Gordon field quantization
I am reading through Dr. Schwartz's book on quantum field theory; in section 2.3.1, he writes the following relation: $$\langle\mathbf{p}|\mathbf{k}\rangle=2\omega_p(2\pi)^3\delta^3(\mathbf{p}-\mathbf{...
- 3,967
4
votes
3
answers
472
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Infinite correlation functions in free field theory
In a free scalar field theory, Wick's theorem guarantees that $\langle \hat\phi(x)\rangle = 0$ and $\langle \hat\phi(x)^2\rangle = \infty$. Given that $\hat \phi(x)$ creates a particle at $x$, these ...
- 200
1
vote
1
answer
153
views
Is this integral always equal to 1?
This is my Hamiltonian. $\psi_{\alpha}$ is a bosonic field.
$$H_{\alpha}=\int \mathrm{d} \mathbf{r} \psi_{\alpha}^{\dagger}(\mathbf{r})\left(-\frac{\nabla^{2}}{2 m}\right) \psi_{\alpha}(\mathbf{r})+\...
- 199
5
votes
1
answer
971
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Weinberg QFT 1 Normalization one 1 particle states p. 66
I encounter a question regarding the derivation of the normalization of 1 Particle states in Weinbergs book (Formula 2.5.14).
Similar questions were asked in A question on page 65 of Weinberg's ...
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