All Questions
Tagged with quantum-field-theory operators
715
questions
9
votes
1
answer
3k
views
Definitions of the Normal Ordering Operator in CFTs and QFTs
Recall the normal ordering of bosonic operators in QFT is defined by a re-arrangement of operators to put creation operators to the left of annihilation operators in the product. This is designed to ...
- 4,176
5
votes
4
answers
2k
views
Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations
Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression:
$\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$
where, ...
- 301
4
votes
2
answers
768
views
Ordering Ambiguity in Quantum Hamiltonian
While dealing with General Sigma models (See e.g. Ref. 1)
$$\tag{10.67} S ~=~ \frac{1}{2}\int \! dt ~g_{ij}(X) \dot{X^i} \dot{X^j}, $$
where the Riemann metric can be expanded as,
$$\tag{10.68} ...
- 1,815
18
votes
1
answer
9k
views
Why/How is this Wick's theorem?
Let $\phi$ be a scalar field and then I see the following expression (1) for the square of the normal ordered version of $\phi^2(x)$.
\begin{align}
T(:\phi^2(x)::\phi^2(0):) &= 2 \langle 0|T(\...
- 4,619
6
votes
1
answer
835
views
How do we measure $i[\hat\phi(x),\hat\phi(y)]$ in QFT?
What operational procedure is required to measure $i[\hat\phi(x),\hat\phi(y)]$ in an interacting (or non-interacting) QFT? [assume smearing by test-functions, or give an answer in Fourier space, for $...
- 9,948
5
votes
1
answer
1k
views
The difference between projection operators and field operators in QFT?
Is there a good reference for the distinction between projection operators in QFT, with an eigenvalue spectrum of $\{1,0\}$, representing yes/no measurements, the prototype of which is the Vacuum ...
- 9,948
9
votes
3
answers
936
views
Regularisation of infinite-dimensional determinants
Can a regularisation of the determinant be used to find the eigenvalues of the Hamiltonian in the normal infinite dimensional setting of QM?
Edit: I failed to make myself clear. In finite dimensions,...
- 7,036
13
votes
1
answer
5k
views
Time-ordering vs normal-ordering and the two-point function/propagator
I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...
- 9,581
43
votes
2
answers
10k
views
Equivalence of canonical quantization and path integral quantization
Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance
$$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t \...
- 5,277
19
votes
3
answers
5k
views
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