All Questions
43
questions
6
votes
4
answers
623
views
How can a QFT field act on particle states in Fock space?
Recently I asked a question that was considered a duplicate. However I felt that the related question didn't answer my doubts. After a bit of pondering I have realized the core of my discomfort with ...
- 4,577
4
votes
0
answers
106
views
How to interpret QFT fields (in relation with QM)? [duplicate]
In QM we deal with the Schrödinger equation:1
$$i\frac{\partial}{\partial t}\psi = H \psi$$
the wave function $\psi(x)$ is the main object of interest: it can be interpreted as a scalar field, in the ...
- 4,577
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
179
views
Existence and uniqueness of vacuum of fermion or boson operators
Suppose I have a set of boson (or fermion) annihilation operators $\{a_i\}$ defined on a Hilbert space. These operators satisfy the canonical (anti-)commutation rules
$$
\text{boson:} \quad [a_i, a^\...
- 660
2
votes
1
answer
224
views
Ground state of Bogoliubov quasi-particles (simpler version)
This is a simplified version of one of my previous questions. Let $b_1, b_2$ be two boson operators; their vacuum is denoted as $|0\rangle$, i.e. $b_i |0\rangle = 0$. We can make a canonical ...
- 660
1
vote
0
answers
47
views
Defining normal distribution in canonical quantization
For simplicity, let us suppose quantized scalar field
$$\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
0
votes
1
answer
107
views
Does particle creation and annihilation in QFT correspond to changing eigenvalues?
If I understood correctly from Griffiths' explanation of the ladder operators as applied to the quantum harmonic oscillator, the ladder operators represent increasing/decreasing the energy level of ...
- 2,327
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
1
vote
0
answers
31
views
Quasi-periodic motion of $N$-particle systems [closed]
My question is about the time evolution of multi-particle systems in QFT. There are such systems evolving a-periodically. I struggle with the treatment of them, always obtaining periodic or quasi-...
- 11
1
vote
1
answer
146
views
Interpretation of field quantization
In the book on Quantum Field Theory by Peskin and Schroeder, it is explained how the field is promoted to an operator, now my question is that in Quantum Mechanics, operators act on kets, what does ...
- 70
0
votes
1
answer
576
views
Anticommutation relations for fermionic operators in Fock space
In second quantization, creation and annihilation operators are defined on Fock space as follows:
\begin{align}
\begin{cases}a_j^\dagger|n_1,n_2,...,n_j,...\rangle=\xi^{s_j}\sqrt{n_j+1}|n_1,n_2,...,...
- 89
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
1
vote
2
answers
171
views
Canonical quantization and the parallels between QFT and QM [closed]
Questions similar to this have been asked multiple times on stack exchange about quantum field theory and the role of operators and the similarity of the theory to regular quantum mechanics. However, ...
- 1,747
1
vote
1
answer
71
views
Why do we get extra symmetric terms/factors when applying annihilation operators to multiparticle states of definite momentum?
Sorry for the wordy title, but I wasn't sure how else to express what I want to ask succinctly.
My question is best illustrated with an example. Suppose we are calculating a scattering amplitude in ...
- 145
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 ...
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