All Questions
24
questions
1
vote
0
answers
90
views
In the path integral formulation of QFT, how do we get quantized particles out of a field?
Every QFT textbook starts by basically postulating that we have discrete states connected by creation and annihilation operators. In Quantum Mechanics, we started from a differential equation and ...
- 1,262
1
vote
1
answer
332
views
How is the interacting vacuum defined in QFT?
I have seen this in a couple of textbooks (Schwartz and Zee), where the author would use the interacting vacuum $|\Omega \rangle$ in a calculation, but would never mention how the state is defined.
...
- 1,896
7
votes
4
answers
965
views
Wavefunction of a particle decay
Lets say we have a decay of $\rho^{0}$, in the following way. $$\rho^{0} \to \pi^{+} + \pi^{-}.$$
Is the following statement true?
$$|\rho^{0}\rangle = |\pi^{+}\rangle|\pi^{-}\rangle.$$
I don't think ...
- 299
4
votes
3
answers
2k
views
In quantum field theory, why is vacuum considered to have the same properties as a particle?
Quotation from the Wikipedia article about vacuum energy:
"The theory considers vacuum to implicitly have the same properties as a particle, such as spin or polarization in the case of light, ...
- 77
4
votes
1
answer
225
views
Do QFTs with a physical cut-off not respect the postulates of Quantum Mechanics?
Wilsonian renormalization says that it's fine to have a physical cut-off. But I am thinking that such theories do not respect the postulates of Quantum Mechanics. Is this true?
Theories with a ...
- 6,355
0
votes
1
answer
165
views
Completeness relation for Hilbert space in quantum field theory
I'm studying chapter 7 section 1 of Peskin and Schroeder. On page 212, we have the one particle Hilbert space $$\tag{7.1} (1)_{\text{1-particle}}=\int \frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}|p\rangle\...
- 789
5
votes
1
answer
384
views
Is it just a mnemonic to call $\phi (x)|0\rangle$ a particle at position $x$?
We often take $\phi (x) |0\rangle$ to mean preparing a particle at position $x$. We also take $\langle 0|\phi(x) \phi(y)|0\rangle$ to mean the probability of creating a particle at $y$ and observing ...
- 6,355
0
votes
0
answers
25
views
Is the dimensionality of a quantum field proportional to the amount of particles? [duplicate]
This is a very basic question about quantum physics (I'm not a physicist).
My understanding from classical field theory is that there is one field of a given type. E.g. there is one gravitational ...
- 1,772
0
votes
2
answers
104
views
What is the role of Hermitian Hamiltonians in relativistic QFT?
In single-particle quantum mechanics, the probability of finding the particle in all space is conserved due to the hermiticity of the Hamiltonians (and remains equal to unity for all times, if ...
- 11.8k
3
votes
3
answers
1k
views
How do the fundamental quantum fields create particles?
According to QFT, particles are excitation of their respective fields (electrons are the excited quanta of the electron field, photons for the electromagnetic field, etc). This excitement is due to ...
- 49
3
votes
0
answers
97
views
Adiabatic turn-on of free multi-particle states
Consider a second-quantized operator $\mathcal{H}_{full}$ describing some interacting QFT, whose action is known on a set of Fock states $\{\mathcal{|F\rangle}\}$, which, in turn, are the eigenstates ...
- 2,921
1
vote
2
answers
213
views
Definition of single-particle states in the free theory
I like defining single-particle states as simultaneous eigenstates of generators of the Poincare group (basically, the representations of the Poincare group).
This is the most fundamental definition ...
- 2,921
9
votes
1
answer
317
views
About Itzykson and Zuber's proof of Goldstone's theorem
In chapter 11-2-2, I&Z discuss Goldstone's theorem. They start by claiming that if an operator $A$ exists, such that
$$ \delta a(t) \equiv \langle 0| [Q(t),A]|0\rangle \neq 0 \tag{11-30} $$
the ...
- 2,648
0
votes
0
answers
177
views
Confusion on the proof of Goldstone’s theorem
I amd reading a proof Goldstone’s theorem in Zee's QFT book. On page $228$, Zee presents the proof as follows.
The conserved charge $Q$ is given by
\begin{equation}
Q=\int d^D\vec{x}J^0(t,\vec{x}).
\...
- 995
3
votes
0
answers
38
views
Parton distribution function in terms of Fock space kets
To my understanding, I can (at least, formally) express the (unnormalized) PDF for a certain constituent of a composite state as
$$
f(x)=f\left(\dfrac{k}{K}\right)=\sum_j m_j^{(k)}|\langle\psi_j^{(k)}|...
- 2,921