All Questions
72
questions
0
votes
1
answer
44
views
Bogoliubov transformation of Bunch-Davies vacuum
Let $\left|0\right>$ be the Bunch-Davies vacuum state of a QFT, for example a free scalar field, in de Sitter space. The creation and annihilation operators w.r.t. this state is a vacuum, i.e. $a^...
- 505
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
225
views
Poincaré invariance and uniqueness of vacuum state
I'm trying to understand the Poincaré invariance of the vacuum state in Minkowski spacetime, how it implies the uniqueness of the vacuum state, and why there's no unique vacuum state in general ...
-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
117
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Problem with understanding the concept of vacuum state of a quantum field
The vacuum state is the state with the minimum energy, which implies no excitations, which I assume is the same as a state with no particles. Then I am confused about a static electric coulomb field. ...
- 795
-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
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
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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
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
3
votes
2
answers
363
views
Proof that asymptotic particle states are free
In quantum field theory, It’s often said that the interacting annihilation operator (defined by the Klein Gordon inner product between the interacting field and a plane wave) behaves like the free ...
user310742
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
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
3
votes
1
answer
445
views
Asymptotic states in the Heisenberg and Schrödinger pictures
One can show that, in the interacting theory, the operators that create single-particle energy-momentum eigenstates from the vacuum are
\begin{align}
(a_p^{\pm\infty})^\dagger=\lim_{t\to\pm\infty}(...
- 1,060
1
vote
0
answers
110
views
Defining Wick/normal ordering beyond rearranging the order of annihilation and creation operators [duplicate]
Most introductory quantum field theory books define Wick ordering as rearranging a product of creation and annihilation operators such that all the creation operators appear to the left of any ...
- 3,350