All Questions
Tagged with quantum-field-theory hilbert-space
681
questions
0
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154
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Peskin & Schroeder equation (7.2)
I found this completeness relation of momentum eigenstate $|\lambda_p\rangle$
Here $|\Omega\rangle$ is the vacuum, and $|\lambda_p\rangle$ represents the state with one particle labeled by $\lambda$ ...
- 1
2
votes
0
answers
77
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LSZ theorem for trivial scattering
The $1\to1$ scattering amplitude is trivial and is given by (take massless scalars for simplicity)
$$
\tag{1}
\langle O(\vec{p}) O^\dagger(\vec{p}\,')\rangle = (2 | \vec{p}\,|) (2\pi)^{D-1} \delta^{(...
- 181
2
votes
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81
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Why Fock representation holds only in a free quantum field theory?
With a quantum system with $N$ degrees of freedom, all the representations are unitarily equivalent to Fock representation. However, if the number of degrees of freedom goes to infinity, there are ...
- 159
-3
votes
1
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91
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Some calculation in Mahan book, p73 [closed]
On page 73 of Mahan, Many-particle physics, 3rd edition, one finds
$$
_0\langle|S(-\infty,0) = e^{-iL}_0\langle|S(\infty,-\infty)S(-\infty,0).
$$
I'm wondering why this is true, as in the previous ...
- 793
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1
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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
9
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4
answers
3k
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If quantum fields are operator valued distributions, why aren't they always smeared?
I don't completely understand the distributional character of a quantum field because I never see them "smeared" in basic textbooks. As I understand it, if $\chi : \mathcal{F} \rightarrow \...
- 615
-1
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1
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249
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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
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1
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114
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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
-2
votes
1
answer
144
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Does the QFT Klein-Gordon equation describe the state of the field or the field operator?
In the canonical quantization of QFT we talk about:
states representing a field.
field operators.
The quantum Klein-Gordon equation is expressed in terms of the field φ. Is φ (in the equation) the ...
- 454
3
votes
1
answer
153
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Equivalence of Schrödinger operator formalism and Path Integral Formulations for Scalar Field Theory
I'm exploring the deep connections between different formulations of quantum field theories and have a specific question about the equivalence between the Schrödinger representation and the path ...
- 1,548
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1
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64
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The relation between spin and momentum in particle state
In quantum field theory, it seems that when we consider a massive particle's spin degree of freedom, we usually do in the particle's rest frame. And I know the little group will only change spin DOF ...
- 35
2
votes
1
answer
284
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How to derive the Fermion generating function formally from operator formalism?
The generating functionals for fermions is:
$$Z[\bar{\eta},\eta]=\int\mathcal{D}[\bar{\psi}(x)]\mathcal{D}[\psi(x)]e^{i\int d^4x
[\bar{\psi}(i\not \partial -m+i\varepsilon)\psi+\bar{\eta}\psi+\bar{\...
- 619
1
vote
0
answers
73
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Convergence of series of elements in a quasi-local algebra
I am studying the quasi-local algebra on Bratteli and Robinson Operator Algebras and Quantum Statistical Mechanics, but there is one thing that is not clear to me at the moment. Let's say that the ...
- 159
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1
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106
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How does Weinberg definition of particle states from standard momentum work?
In his first volume, part 2.5, Weinberg define one particle states $Φ_{p,𝜎}$ ($p$ is the momentum and $𝜎$ another quantum number) in the following way :
Choose a Standard momentum $k$
Find a ...
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