All Questions
20
questions
2
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2
answers
124
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Dictionary between interpretations of field operators
For now, let $\hat{\phi}(x)$ be a quantization of a classical, real scalar field $\phi(x)$.
My understanding is that, for fixed $x$, there are three ways to regard the operator $\hat{\phi}(x)$:
The ...
2
votes
1
answer
88
views
Why reasonable observables are made of an even number of fermion fields?
On Michele Maggiore book on QFT (page 91) is stated, out of nothing, that "observables are made of an even number of fermionic operator" and similar sentences is in Peskin book (page 56).
Is ...
- 613
7
votes
1
answer
495
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What exactly is the difference between the position operator in non-relativistic QM and the Newton-Wigner operators in QFT?
I've read several threads over the past several days talking about how photons don't have wavefunctions in the same way as massive particles do because they don't have non-relativistic limits. If I ...
- 2,327
0
votes
1
answer
165
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Fields as Hermitian operator [duplicate]
In QFT fields are Hermitian operators. And observables are represented by operators. I am confused are fields also observables?
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12
votes
2
answers
2k
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How to interpret quantum fields?
As an analogy of what I am looking for, suppose $f(x,t)$ represents a classical field. Then we may interpret this as saying at position $x$ and time $t$ the field takes on a value $f(x,t)$.
In quantum ...
- 3,350
5
votes
0
answers
255
views
Observables and local observations in quantum field theory
I have recently taken a quantum field theory course at my university but it focused heavily on the mathematics of the theory and not the physics. So I am left with a few questions on observables and ...
- 1,747
1
vote
2
answers
832
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Are quantum fields observable? [duplicate]
I have an elementary question. In quantum field theory observables are operators. But the quantum fields are operators too. This means the quantum fields are observable? I read somewhere that quantum ...
- 366
3
votes
1
answer
361
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Is there an alternative to Fock Space and Hilbert Space in quantum field theory? [duplicate]
Why were Fock Space and Hilbert Space used in quantum field theory?
What was the motivation for choosing them over other mathematical techniques?
user291777
0
votes
1
answer
147
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What are the operators associated to the electron/electromagnetic quantum field?
After reading through a number of questions on SE including What are field quanta? and What are quantum fields mathematically?, I am still struggling with what specific operators are associated to ...
- 229
5
votes
2
answers
256
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Confusion about quantum field in AQFT
As far as I known, quantum field is defined by operator-valued distribution mathematically. If I understand correctly, in AQFT, we use self-adjoint elements of $C$* algebra to describe algebra of ...
- 525
11
votes
4
answers
2k
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Why are quantum mechanical observables time-independent?
I am aware of the two pictures, namely the Schrödinger and Heisenberg pictures, where the time dependence is carried by the state in the former and by the operator in the latter. However, why does it ...
- 1,325
2
votes
0
answers
218
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What significance do field-operators have, if they don't correspond to observables because of non-hermicity?
Since field-operators are not always hermitian (for example in case of a complex scalar field, or the dirac-field), they don't (in the quantum-mechanical sense) correspond to observables.
Does that ...
- 6,763
1
vote
1
answer
65
views
Observing the conserved canonical momenta
Suppose I have a Lagrangian $\mathcal{L}[\phi]$ with $\phi$ a cyclic variable, which means that the Lagrangian is symmetric under shift of $\phi\rightarrow\phi+c\quad$.
The equation of motion will be ...
- 1,874
6
votes
1
answer
817
views
What are the orthogonal eigenstates of the field operator?
In Peskin & Schroeder section 9.2, they derive the two-point function in the path integral formalism:
$$\langle \Omega | \mathcal{T} \left\{ \hat{\phi}(x_1)\hat{\phi}(x_2)\right\} | \Omega \rangle ...
- 1,138
2
votes
3
answers
3k
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How to write an operator in matrix form?
Say I have the following operator:
$$\hat { L } =\hbar { \sum_{ \sigma ,l,p } { l } \int_{ 0 }^{ \infty }\!{ \mathrm{d}{ k }_{ 0 }\,\hat { { { a }}}_{ \sigma ,l,p }^{ \dagger } } } \left({ k }_{...
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