市民在丹轩梓园买新房 进户水管爆裂刚装修好房子被淹
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Results tagged with operators
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user 219346
百度 无论房地产税何时推出，可以肯定的是，房地产税一定是先立法后实施。
In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
2
votes
Accepted
Derivation of $T(z)(TT)(w)$ in CFT
Some introductory sources are too quick to say that only singular terms matter in chiral OPEs. Yes, meromorphic functions are determined by their singularities but it may well be the case that one nee …
- 10.8k
3
votes
Accepted
Extracting the central charge from correlation functions and normalization of operators
The most common convention is to have unit normalization for all operators that are not currents. …
- 10.8k
3
votes
Accepted
OPE Coefficients from two and three point functions
If you take the multi-variable Taylor expansion
\begin{equation}
f(x) = f(0) + x^\mu \partial_\mu f(0) + \frac{1}{2} x^\mu x^\nu \partial_\mu \partial_\nu f(0) + \dots
\end{equation}
and apply it to t …
- 10.8k
10
votes
Accepted
What's the (intuitive) difference between a primary and a quasi-primary operator in a CFT?
As Prahar mentioned, operators that transform as a highest weight of the "X algebra" are called "X primary". … So in non-supersymmetric 2d CFTs, where you have the global algebra ($SL(2, \mathbb{C})$) and the local algebra (Virasoro), there are two types of primary operators. …
- 10.8k
4
votes
Accepted
Omitting regular terms in OPE
"We can ignore regular terms in an OPE" is often made as a blanket statement but we need to be more careful. It's better to say that we can do this if we're trying to compute correlation functions of …
- 10.8k
0
votes
Hermitian conjugation of vector operators in radial quantization
Do we know that
\begin{align}
O^\dagger_{\text{cyl}}(\tau, \textbf{n}) = O_{\text{cyl}}(-\tau, \textbf{n})
\end{align}
for operators of any spin? … Sorting operators into representation that have their spin parts under inversions fully determined is something you need conformal invariance to do. …
- 10.8k
5
votes
Accepted
Mode expansion of vertex operator in $c=1$ CFT at rational radius?
If your extra currents have spin 1 then you're in the case Prahar mentions which is $R^2 = 1$ (in $\alpha' = 1$ units) and a chiral algebra of $\mathfrak{su}(2)_1$.
The more general case has the spin …
- 10.8k
1
vote
Why is OPE associativity valid?
Your statement that the OPE in one channel converges if and only if the other diverges is incorrect. Choosing the points in your example to be
\begin{equation}
x_1 = (z, \bar{z}), \; x_2 = 0, \; x_3 = …
- 10.8k
1
vote
Bra-ket representation of projection operators
Operators that can be diagonalized look like
\begin{align}
P = \sum_i p_i \left | \psi _i \right > \left < \psi_i \right |
\end{align}
in their own eigenbasis. …
- 10.8k
2
votes
Accepted
Why convention for Heisenberg algebra?
I think the convention is to use operators which are Fourier modes of the most basic fields you want to work with. …
- 10.8k
3
votes
2D CFT correlator involving stress tensor and current
$F_2$ is correct and indeed it is most easily found with
\begin{align}
\langle TJO_1O_2 \rangle &= \left [ \frac{1}{(z-w)^2} + \frac{h}{(z - x_1)^2} + \frac{h}{(z-x_2)^2} \right ] \langle JO_1O_2 \ran …
- 10.8k
1
vote
How this limiting procedure defines an operator in the state-operator map?
To make sense of Polchinski's derivation with the unit disk, I like to consider a correlator of operators where the largest radial co-ordinate involved is $1$. … At this point, we can use the fact that specifying operators is the same as specifying their matrix elements. …
- 10.8k
2
votes
Why does a normal ordered product of operators (in CFT) have 0 expectation value?
From this perspective, it doesn't matter whether $O(x)$ happens to be the normal ordered product of two other operators or not. … But more generally, the modes with $n > -h$ have to be annihilation operators because
\begin{equation}
O(z) = \sum_n O_n z^{-n-h}
\end{equation}
and we need $O(0)$ to be able to act on the vacuum and not …
- 10.8k
1
vote
Infinitesimal generator
When you wrote the generators as differential operators, this was just the orbital part. The term you dropped was the spin part. …
- 10.8k
2
votes
Accepted
Correlation function of normal-ordered fundamental fields in the $SU(3)_1$ WZW model
The main facts being used are:
Holomorphic operators need to have integer or half-integer $\Delta$ because general operators need to have integer of half-integer $h - \bar{h}$. … Normal-ordered holomorphic operators are still holomorphic. …
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