All Questions
132
questions
0
votes
1
answer
79
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Regarding Energy Eigenstate and Position Eigenstate
I am solving problem 14.4. (a) of Schwartz's Quantum Field Theory and the Standard Model. It is related to the simple harmonic oscillator in quantum mechanics. It asks the eigenstate of the position ...
- 79
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
0
answers
64
views
Operator that gives a permutational symmetry factor
Suppose that we have a system with $N$ bosonic modes, meaning that there is a vacuum state $|0\rangle$ and a set of $N$ pairs of creation-annihilation operators $a_i$ and $a^{\dagger}_i$. When ...
- 31
1
vote
1
answer
85
views
What determines the conjugation of a state in quantum field theory?
In basic quantum mechanics, we define the inner product between two states $\phi$ and $\psi$ as $\phi^\dagger \psi$, where $\phi^\dagger$ is the conjugate transpose of the vector $\phi$. However in ...
- 2,504
2
votes
0
answers
81
views
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
1
vote
0
answers
73
views
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
3
votes
0
answers
115
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What is the single-particle Hilbert space in the Fock space of QFT?
In Quantum field theory, the fields are operator-valued functions of spacetime. So for a scalar (spin $0$) field $$\psi: \mathbb{R}^{3,1} \rightarrow O(F),$$ where $O(F)$ is the space of operators on ...
- 51
1
vote
0
answers
34
views
Normalisation for a two fermion state
I'm trying to follow this paper (Fermion and boson beam-splitter statistics. Rodney Loudon. (1998). Phys. Rev. A 58, 4904)
However, I don't quite understand where some of his results come from.
...
- 33
0
votes
1
answer
115
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Quantum field theory states
I've been told that in QFT, everything is turned into their continuum type, i.e:
$$q_i \to \phi(x)$$
$$p_i \to \pi(x)$$
$$[q_i, p_j] = i\delta_{ij} \to [\phi(x), \pi(y)] = i\delta(x-y)$$
etc.
Now I've ...
- 1,324
2
votes
1
answer
119
views
Understanding mathematically the promotion of field/observable to operator in QFT
First, I know it "worked", in physics sense.
My question is what happened in the math sense.
When promoting something, such as a field, to an operator, am I essentially mapping the field to ...
- 63
2
votes
2
answers
867
views
What does sandwiching with an unitary operator and its inverse imply?
I am following the book "An introduction to quantum field theory" by Peskin and Schroeder. In the section 'Discrete symmetries of the Dirac theory', it is written,
$P a^s _p P^{-1} = \eta_a ...
- 399
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
90
views
Does "completeness" of operator fields in QFT have a counterpart in non-relativistic QM?
In section II.1.2 of Haag's Local Quantum Physics, he lists the Wightman axioms of QFT, in particular describing an axiom (F) called "completeness":
F. Completeness. By taking linear ...
- 3,407
4
votes
1
answer
225
views
Do QFTs with a physical cut-off not respect the postulates of Quantum Mechanics?
Wilsonian renormalization says that it's fine to have a physical cut-off. But I am thinking that such theories do not respect the postulates of Quantum Mechanics. Is this true?
Theories with a ...
- 6,355