All Questions
20
questions
0
votes
1
answer
59
views
Concrete understanding of QFT Hilbert space for spinor
I'm trying to understand the concepts of a spinor field in QFT. I naively understand there are two values at each spatial position $\vec{r}$: a probability amplitude and a spinor value. Is there a ...
- 148
8
votes
1
answer
402
views
The wave-function in QFT
As I understand, the wave-function in QFT becomes a wave-functional dependent on fields. I have heard this told by Sean Carroll in his Biggest Ideas in the Universe lectures. Srednicki gives the $n$-...
- 525
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
0
votes
1
answer
210
views
In what way does QFT combine particles' wavefunctions to form fields?
If I understand correctly, in terms of the math of QFT, saying that particles are excitations in fields is mathematically equivalent to saying that a field is a representation of all possible ...
- 2,327
8
votes
3
answers
796
views
What are the adequate Hilbert spaces for Schrödinger, Schrödinger–Pauli, Dirac equations, and QFT?
In quantum mechanics (both non-relativistic and relativistic), it is possible to study physical systems by looking for solutions of PDEs, whose solutions belong to suitable Hilbert spaces:
...
- 1,640
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
1
answer
110
views
Is the quantum mechanical wavefunction a sum of amplitudes in QFT?
I can remember while reading Ryder's book on quantum field theory, i a chapter intro, that Dyson remembered Feynman saying that an electron does anything it likes. It moves at any speed, in any ...
0
votes
0
answers
112
views
Motivation for Quantum Field Operators
I am currently learning quantum field theory and trying to wrap my head around a couple of concepts that are still eluding my understanding:
What is the reason for transitioning from wavefunctions to ...
- 329
0
votes
0
answers
80
views
Wave function symmetry on Fock space
Let's consider two electrons, created in the following manner
$c^{\dagger}_{k_1,u} c^{\dagger}_{k_2,d} |0\rangle$,
where $k_1$ and $k_2$ are the wavenumbers, and $u$ and $d$ stand for up and down spin ...
- 87
2
votes
1
answer
93
views
How does $\sum_k \psi_k^*(\vec{r})\psi_k(\vec{r}')=\delta(\vec{r}-\vec{r}')$ express the completeness of a basis?
The annihilation field operator is defined as
$$\hat{\psi}(\vec{r})=\sum_k \hat{b}_k \psi_k(\vec{r})$$
Two of these operators satisfy the commutation relations
$$[\hat{\psi}(\vec{r}),\hat{\psi}^{\...
- 1,581
4
votes
2
answers
312
views
Hilbert space and wave functions of single-particle states in QFT (Weinberg)
So, following Weinberg (chapter 2), he derives all the transformation properties of the states $\Psi_{p,\sigma}$. These are eigenstates of the four-momentum (and some other observable with a discrete ...
4
votes
2
answers
196
views
Why is it useful to characterize relativistic particle states by this kind of wavefunction?
This question is a followup to my previous one "Why are momentum eigenstates in QFT plane waves?
" as it made sense for me to ask this separately, in a self-contained manner.
In QFT we have ...
user303517
0
votes
0
answers
173
views
Multi-mode Fock states
I would like to ask if this expression makes sense.
$$|Ψ⟩ = \frac{1}{\sqrt{7}}(|1000000⟩+|0100000⟩+|0010000⟩+|0001000⟩+|0000100⟩+|0000010⟩+|0000001⟩)$$
For example, $|1000000⟩$ represents one particle ...
1
vote
1
answer
75
views
What are we measuring in a quantum field when we square the wavefunction?
Suppose we are doing a measurement in a particular quantum field, i.e electron field. Are we looking for the probability of the electron to show up at that spot we are measuring or are we measuring ...
- 13k
3
votes
2
answers
881
views
Explicit form of the wavefunctional
In quantum mechanics, one in principle can write down an explicit form of the corresponding wave-function. For example, $V_i$ for the $i$-th level of quantum harmonic oscillator.
In QFT, the Hilbert ...
