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Results tagged with mp.mathematical-physics
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user 36688
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
3
votes
Generalization of Curl to higher dimensions
The curl of a vector field $X=P\partial_x+Q\partial_y+R\partial_z$ is equal to
$$
\mathrm{Curl}(X)= (R_y-Q_z)\,\partial_x +(P_z-R_x)\,\partial_y+ (Q_x-P_y)\,\partial_z
$$
For the moment we repla …
- 356
1
vote
1
answer
213
views
Some quantities which definitions are (somehow) similar to the classical Divergence
Motivated by classical formulas $L_{X}=d\circ i_{X}+i_{X}\circ d$ and $L_{X} \Omega=Div(X) \Omega$ and the essential role of the diff operator $d$ in definition of divergence, we define some …
- 356
4
votes
0
answers
326
views
The Moyal action of a planar vector field
Let $X=P\frac{\partial}{\partial x}+Q\frac{\partial}{\partial y}$ be a polynomial vector field on $\mathbb{R}^{2}$. Consider the following (Moyal) operator on $\mathbb{C}[x,y]$:
$\tilde{D}_{X}(f) …
- 356