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Results tagged with operators
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user 259376
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 $\times$, $+$!
1
vote
0
answers
50
views
Expansion of trace of operator
I am looking for a way to rewrite this trace "at leading order in $a$"
$$
\text{Tr}(-a\nabla^2+A(r))
$$
Would it be possible to expand this trace if my parameter $a$ is small, $a<<1$ (which is the cas …
3
votes
1
answer
74
views
Infinitesimal generator
From Conformal field theory (Di Francesco, Pierre Mathieu):
We now study the effect of infinitesimal transformations on the action. Such transformations may in general be written as
$$
\begin{aligned …
0
votes
1
answer
72
views
Hausdorff formula for Dilatation operator
Using the Hausdorff formula I can find the dilation operator at all position:
$$
e^{i x^\rho P_\rho} D e^{-i x^\rho P_\rho}=D+\left[D,-i x^\rho P_\rho\right]+\frac{1}{2}\left[\left[D,-i x^\rho P_\rho\ …
1
vote
0
answers
144
views
Scalar Yukawa theory, contraction
In the scalar Yukawa theory ($\Phi$ is real scalar field and $\phi$ is a complex scalar field):
\begin{equation}
\mathcal{L}_{S Y}=\left(|\partial \phi|^{2}-m^{2}|\phi|^{2}\right)+\frac{1}{2}\left((\p …