All Questions
51
questions
3
votes
1
answer
249
views
Derivation of two-body Coulomb interaction in momentum space
$\newcommand{\vec}{\mathbf}$
In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
0
votes
2
answers
88
views
Ladder operators and creation & annihilation operators - different between $a$, $b$ and $c$ [closed]
Usually, the ladder operator denoted by $a$ and $a^\dagger$. In some case, people talk about the creation operator and denote it by $c$ and $c^\dagger$. Recently I see another notation, $b$ and $b^\...
- 23
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
3
votes
3
answers
815
views
Transition from position as operator in QM to a label in QFT
In David Tong's lecture "Quantum Field Theory" - Lecture 2, he said that
"In Quantum mechanics, position is the dynamical degree of the particle which get changed into an operator but ...
user385554
1
vote
2
answers
188
views
Squared spin operators in second quantization
Spin operator in second quantization can be written as:
\begin{equation}
\hat{\vec{S}}_{i} = \frac{1}{2} \sum_{\sigma \sigma'} \hat{c}^{\dagger}_{i\sigma} \hat{\vec{\sigma}}_{\sigma \sigma'} \hat{c}_{...
- 13
2
votes
1
answer
143
views
How is a Fock state from QFT related to the wave function from quantum mechanics?
I am currently studying quantum field theory as part of my degree. I'm just lacking intuition or an understanding of some basic concepts. So please don't hesitate to correct me if i got something ...
- 29
4
votes
2
answers
248
views
Quantization of non-relativistic complex scalar field
I found that the taking the non-relativistic limit of the Lagrgangian for complex scalar fields gives
$$\mathcal{L} = i\dot{\psi}\psi^* -\frac{1}{2m}\nabla\psi \nabla\psi^*.\tag{1}$$
Now, when we ...
- 193
5
votes
1
answer
510
views
The underlying cause of ill-defined loop-integrals in Quantum Field Theory
One of the main causes which leads to ill-defined loop integrals in Quantum Field Theory is that the variables of a Field Theory, $\varphi(x)$ for instance, are Quantum Fields which are governed by ...
- 9,778
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
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
1
vote
2
answers
137
views
Motivation behind introducing creation/annihilation operators into the Dirac equation
When studying the Klein-Gordon equation, the introduction of creation/annihilation operators was justified by recognizing a harmonic-oscillator-like equation which we know how to quantize. Is there a ...
- 3,350
2
votes
1
answer
202
views
Is there a way to fix the ordering ambiguity of canonical quantization?
This question arose from my question on whether the vacuum energy is actually present for a free quantum scalar field
What is the right way to treat the vacuum energy?
Part of this discussion is that ...
- 705
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
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
1
vote
1
answer
235
views
Two-particle operators in QFT and the factor 1/2
I am learning about QFT through the book Quantum Field Theory for the Gifted Amateur and I am having trouble understanding the factor 1/2 in the definition of two particle field operators. In the book ...
- 203