All Questions
25
questions
1
vote
0
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47
views
Defining normal distribution in canonical quantization
For simplicity, let us suppose quantized scalar field
$$\hat{\phi}=\int{\frac{d^3p}{\left(2\pi\right)^32E_\vec{p}}\left(a_\vec{p}e^{-ipx}+b^\dagger_\vec{p}e^{ipx}\right)}$$
How does one add a particle ...
- 925
1
vote
0
answers
89
views
LSZ Reduction Formula (Weinberg Derivation)
In section 10.3 of Weinberg's Volume 1 in deriving LSZ reduction Formula, the author says,
We also define a 'truncated' matrix element $M_l$ by
$$\int d^4 x_2 \cdots e^{-q_2x_2} <\textbf q \sigma| ...
- 96
1
vote
1
answer
107
views
In which mathematical space do the spinors act on?
I'm studying QFT and from what I've learnt so far is that a general quantum field $\widehat{\phi}(x)$ can be decomposed (at least for the fermion case) as
$$\widehat{\phi}(x)=∫\frac{d^{3}p}{(2\pi)^{3/...
- 475
2
votes
0
answers
78
views
QFT Formalism, Relation between different POVs
A Klein-Gordon field on a Minkowski background can be written in the following expansion
$$ \hat{\phi}(x) = \int \frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}} (\hat{a}_p e^{-ip x} + \hat{a}^\dagger_p e^{...
- 136
5
votes
1
answer
305
views
What does it mean to apply a creation or annihilation operator to a free field, e.g. $\langle 0|a(p)\varphi(x)| 0 \rangle$?
I am self studying Quantum Field Theory, and I am starting to get a little lost. So far, I have studied free fields and some basic computations involving them, such as creation and annihilation ...
- 3,350
2
votes
1
answer
82
views
Explicit formulas for eigenstates of field operators
Let's take the free spin 0 quantum field,
$$\hat{\phi}(\boldsymbol{x},t)=\int d^3p\big(\hat{a}_p u_p(\boldsymbol{x},t)+\hat{a}^\dagger_pu_p^\ast(\boldsymbol{x},t)\big)$$
here $$u_p=\frac{1}{\sqrt{2\...
- 789
0
votes
1
answer
85
views
Why can we arbitrarily set the expectation value of a field operator by representing the field state as a product of coherent states?
In the paper "Unusual Transitions Made Possible by Superoscillations", the author begins by solving for a coherent state \begin{equation}|\alpha\rangle\end{equation} such that
\begin{...
- 325
4
votes
3
answers
551
views
Overlap $\langle \phi|\pi \rangle$ in quantum field theory
I was reading through Kapusta & Gale, "Finite temperature Field theory Principles and applications". In chapter 2, they derive a partition function for a normal field theory (0 ...
- 1,023
0
votes
1
answer
116
views
Is this definition of the Fourier Transform of a quantum field operator rigorous?
Let there be a a quantum field operator $\hat\phi(t,\vec{x})$ which, because it acts (pointwise) on a separable Hilbert space, I expect I can write as
$$\hat\phi(t,\vec{x}) = \sum_n\sum_m\phi^n_m(t,\...
- 34
3
votes
1
answer
636
views
Confusion about modes and quantum field theory
I'm learning quantum field theory from P&S and Srednicki. I'm having a lot of difficulties understanding the concept of a momentum state. In particular, I'm confused about how to interpret the ...
user299467
3
votes
1
answer
449
views
Vacuum energy of a free scalar field from path integral
My question has been asked two other times:
Spinor vacuum energy (misleading title) and
Vacuum Energy Calculation using Path Integral. I am not completely satisfied with the answers and it looks like ...
- 713
4
votes
1
answer
349
views
Individual particle states in Fock space
I am currently learning QFT, and after watching the wonderful lectures by Leonard Susskind (https://theoreticalminimum.com/courses/advanced-quantum-mechanics/2013/fall), I am still struggling to see ...
- 343
5
votes
3
answers
1k
views
About an expression of Peskin and Schroeder
On page 83 of Peskin and Schroeder, they expand an interacting field $\phi(x)$ at a fixed time $t_0$ in terms of the ladder operators as $$\phi(t_0,\vec{x})=\int\frac{d^3p}{(2\pi)^3\sqrt{2E_{\vec{p}}}}...
- 11.8k
3
votes
0
answers
193
views
Interpretation of annihilation and creation operators
If we write some quantum field in a form using creation and annihilation operators we are, in a way, doing a Fourier series with annihilation and creation operators being coefficients. So, if they are ...
- 1,803
0
votes
0
answers
184
views
Transition from phi basis to occupation number in quantum field theory
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 ...
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