The operators tag has no wiki summary.
1
vote
2answers
239 views
Derivatives of operators
How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this?
For example: say you had the ...
2
votes
1answer
40 views
Statistical sum of physical quantities in a quantum system
Let $C = A + B$ (statistical sum, so $\mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]$), and let $p(A = a) = 1$. Are the following true?
$\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$
...
4
votes
0answers
67 views
Shape of the state space under different tensor products
I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this).
Recall: In a ...
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 ...
3
votes
0answers
41 views
Spectrum of a quantum relativistic “distance squared” operator
This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ ...
2
votes
0answers
94 views
How to define the mirror symmetry operator for Kane-Mele model?
Let us take the famous Kane-Mele(KM) model(http://prl.aps.org/abstract/PRL/v95/i22/e226801 and http://prl.aps.org/abstract/PRL/v95/i14/e146802) as our starting point.
Due to the time-reversal(TR), ...
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, ...
1
vote
0answers
26 views
Quantum graph theory: complex spectra
In quantum graph theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? Spectral graph theory is as far as I know a not completely ...
1
vote
0answers
74 views
Explicit evaluation of a radially ordered product
I am trying to understand the application of the operator product expansion to calculate the radially ordered product in the complex plain of $T_{zz}(z)\partial_w X^{\rho}(w)$ which should result in
...
0
votes
0answers
35 views
An application of Toeplitz operators
I want to find an application of the Toeplitz operators. All I need is a known problem (not an open problem) which solution use the theory of Toeplitz operators. I don't need all the details but I ...
0
votes
0answers
38 views
Time ordering and Fermions
Having time ordering operator for fermions, should it reverse sign if it swaps operators with opposite spin variable? In other words should
$T[c_{t_1,\uparrow}c_{t_2,\downarrow}^\dagger]$
return ...
