Tagged Questions
3
votes
0answers
46 views
A particlar normal ordering problem
Say we have an expression of the form:
$$
\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,
$$
where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating ...
1
vote
0answers
36 views
QFT basics for Klein-Gordon fields
I am teaching myself QFT from Peskin for next years maths course and I have two questions:
What is a c-number? Is it a complex number, and if so why does it mean, ...
4
votes
3answers
106 views
Associating a Unitary operator to proper Lorentz transformations?
If one reads eg page 32 of Srednicki where he says:
In quantum theory, symmetries are represented by unitary (or
antiunitary) operators. This means that we associate a unitary
operator U(Λ) ...
1
vote
1answer
96 views
Klein-Gordon Canonical Commutation Relation (CCR)
In the complex Klein-Gordon field we regard as dynamical variables the field $\phi$, the complex conjugate of the field $\phi^*$, and the momenta $\pi$, $\pi^*$. I can't see how should arise the ...
4
votes
2answers
225 views
Eigenvalues of a quantum field?
Fields in classical mechanics are observables. For example, I can measure the value of the electric field at some (x,t).
In quantum field theory, the classical field is promoted to an operator-valued ...
6
votes
1answer
232 views
What is the value of a quantum field?
As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
3
votes
2answers
154 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,
$$\tag{10.68} ...
3
votes
1answer
707 views
Why/How is this Wick's theorem?
Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$.
$$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$
...
4
votes
1answer
226 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 ...
4
votes
1answer
129 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 ...
8
votes
2answers
499 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 ...
