All Questions
40
questions
2
votes
1
answer
76
views
Why does a normal ordered product of operators (in CFT) have 0 expectation value?
Why does a normal ordered product of operators (in CFT) have 0 expectation value?
The definition (Francesco - Conformal field theory pg. 174) of the normal ordered product of two operators $A(z)$ $B(z)...
- 327
4
votes
1
answer
121
views
How do we know at the operator-level that the tadpole $\langle\Omega|\phi(x)|\Omega\rangle=0$ vanishes in scalar $\phi^4$ theory?
I'm a mathematician slowly trying to teach myself quantum field theory. To test my understanding, I'm trying to tell myself the whole story from a Lagrangian to scattering amplitudes for scalar $\phi^...
- 421
1
vote
3
answers
154
views
What does the state $a_k a_l^\dagger|0\rangle$ represent?
Consider the action of the operator $a_k a_l^\dagger$ on the vacuum state $$|{\rm vac}\rangle\equiv |0,0,\ldots,0\rangle,$$ the action of $a_l^\dagger$ surely creates one particle in the $l$th state. ...
- 11.8k
-2
votes
1
answer
74
views
On creation annihilation operators of the free Klein-Gordon field [closed]
I want to calculate multiparticle states like $|\vec p,\vec p\rangle$ from $|0\rangle$. It seems that I would need to compute from things like: $a^{\dagger}_{\vec p}a^{\dagger}_{\vec p}|0\rangle$?
It ...
- 4,399
0
votes
1
answer
66
views
Clarification Needed for The Klein-Gordon Field Acting on the Vacuum State (Peskin and Schroeder)
In Peskin and Schroesder's Introduction to Quantum Field Theory, section 2.3, the Klein Gordon Field has the expression
$$
\phi(x,t) := \int \frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2\omega_{p}}} [a_{...
- 23
1
vote
0
answers
74
views
Doubt regarding use of Wick contractions
I'm currently taking my first course in QFT and am learning about finding transition amplitudes using Wick's theorem. As far as I'm aware, Wick's theorem gives us a way to change from a time-ordered ...
- 139
-1
votes
1
answer
249
views
What does the field operator $φ(x)$ do to the Fock space?
For simplicity: imagine a free, scalar theory, and a 1 particle universe.
Spacetime: we have an operator $φ(x)$ defined everywhere on spacetime.
Fock space: the space of states in which the particle ...
- 454
2
votes
1
answer
154
views
Doubt on scattering amplitude in scalar Yukawa theory
I'm currently following David Tong's notes on QFT. In the section on calculating transition amplitudes using Wick's theorem, he gives an example using a scalar Yukawa theory with real scalar field $\...
- 139
0
votes
1
answer
114
views
Can we construct the QFT Fock space with only field operators $φ(x)$ acting on the vacuum?
We always hear that
The Fock space is constructed with multiple $~a^\dagger_{\vec p}$ acting on the vacuum for different values of ${\vec p}$ (we can use alternatives notations to ${\vec p}$ because ...
- 454
0
votes
0
answers
43
views
Calculation about fermions via quantum field theory
I want to ask a specific question occurred in my current learning about neutrinos.
What I want to calculate is an amplititude:
\begin{equation}
\langle\Omega|a_{\bf k m}a_{\bf pj}a_{\bf qi}^{\dagger}...
- 1
2
votes
0
answers
153
views
Is this formula, other than (2.38) in peskin's quantum field theory, also true?
This is soft interlude question. I am rereading the Peskin & Schroeder's Quantum field theory, p.23, (2.38) and some question arises.
First, let's refer to Lorentz transformations for scalar ...
- 323
0
votes
2
answers
85
views
The vanishing of vacuum expectation value
I have some difficulty understanding why the vacuum expectation value vanishes. As illustrated in my notes, we can split the field into two parts:
$$
\phi(x) = \phi^+(x) + \phi^-(x),
$$
where $\phi^+(...
- 41
7
votes
2
answers
406
views
States created by local unitaries in QFT
In quantum field theory, consider acting on the vacuum with a local unitary operator that belongs to the local operator algebra associated with a region. In such a way, can we obtain a state that is ...
- 1,221
2
votes
1
answer
179
views
Existence and uniqueness of vacuum of fermion or boson operators
Suppose I have a set of boson (or fermion) annihilation operators $\{a_i\}$ defined on a Hilbert space. These operators satisfy the canonical (anti-)commutation rules
$$
\text{boson:} \quad [a_i, a^\...
- 660
-1
votes
1
answer
208
views
Field operators on vacuum
What do the field operators $\psi$ and $\pi$ produce when they act on vacuum $|0>$ state?
Here,
$$\psi(\vec{x}) = \int \frac{d^3p}{(2\pi)^{3}}\frac{1}{\sqrt{2E_p}}\left(a_p e^{i\vec{p}\cdot \vec x} ...
- 21