All Questions
Tagged with quantum-field-theory operators
715
questions
43
votes
2
answers
10k
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Equivalence of canonical quantization and path integral quantization
Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance
$$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t \...
- 5,277
31
votes
3
answers
4k
views
There are too many Wick's Theorems!
This is a follow-up question to QMechanic's great answer in this question. They give a formulation of Wick's theorem as a purely combinatoric statement relating two total orders $\mathcal T$ and $\...
- 7,309
27
votes
4
answers
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How exactly is "normal-ordering an operator" defined?
(In this question, I'm only talking about the second-quantization version of normal ordering, not the CFT version.)
Most sources (e.g. Wikipedia) very quickly define normal-ordering as "reordering ...
- 48.4k
26
votes
2
answers
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Is there any theorem that suggests that QM+SR has to be an operator theory?
UPDATE
To make my question more precise, I'll define what I mean by an operator theory:
An operator theory is a theory in which the dynamical objects are operators, i.e., the equations of motion are ...
25
votes
2
answers
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In what sense is the path integral an independent formulation of Quantum Mechanics/Field Theory?
We are all familiar with the version of Quantum Mechanics based on state space, operators, Schrodinger equation etc. This allows us to successfully compute relevant physical quantities such as ...
- 2,212
24
votes
1
answer
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What does the identity operator look like in Quantum Field Theory?
In texts on ordinary quantum mechanics the identity operators
\begin{equation}\begin{aligned}
I & = \int \operatorname{d}x\, |x\rangle\langle x| \\
& = \int \operatorname{d}p\, |p\...
- 22.7k
23
votes
5
answers
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Why is normal ordering a valid operation?
Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that?
Is its definition motivated by ...
- 2,301
23
votes
2
answers
10k
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Time ordering and time derivative in path integral formalism and operator formalism
In operator formalism, for example a 2-point time-ordered Green's function is defined as
$$\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\theta(x_1-x_2)\phi(x_1)\phi(x_2)+\theta(x_2-x_1)\phi(x_2)\...
- 3,995
21
votes
1
answer
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What happens if we apply time-ordering to Wick's theorem $T\{a,b\}=N\{a,b\}+\langle ab\rangle$?
Let $T\{...\}$ denote time-ordering, $N\{...\}$ normal-ordering and $\left<ab\right>$ be the propagator.
Wick's theorem states that
$$ T\{ab\} = N\{ab\} + \left<ab\right>. $$
I now ...
- 16.2k
21
votes
4
answers
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Schrödinger wavefunctional quantum-field eigenstates
The reason that I have this problem is that I'm trying to solve problem
14.4 of Schwartz's QFT book, which've confused me for a long time.
The problem is to construct the eigenstates of a quantum ...
- 2,071
20
votes
1
answer
6k
views
Why path integral approach may suffer from operator ordering problem?
In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path.
What did ...
- 553
19
votes
3
answers
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What does the ordering of creation/annihilation operators mean?
When a system is expressed in terms of creation and annihilation operators for bosonic/fermionic modes, what exactly is the physical meaning of the order in which the operators act?
For example, for ...
- 1,239
19
votes
3
answers
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Are the path integral formalism and the operator formalism inequivalent?
Abstract
The definition of the propagator $\Delta(x)$ in the path integral formalism (PI) is different from the definition in the operator formalism (OF). In general the definitions agree, but it is ...
18
votes
1
answer
9k
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Why/How is this Wick's theorem?
Let $\phi$ be a scalar field and then I see the following expression (1) for the square of the normal ordered version of $\phi^2(x)$.
\begin{align}
T(:\phi^2(x)::\phi^2(0):) &= 2 \langle 0|T(\...
- 4,619
18
votes
3
answers
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Eigenstate of field operator in QFT
Why don't people discuss the eigenstate of the field operator? For example, the real scalar field the field operator is Hermitian, so its eigenstate is an observable quantity.
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