论文标题
拉格朗日密度的二元数是多少？
What is the quantity dual to the Lagrangian density?
论文作者
论文摘要
我们解决了最近发现的非线性电动力学的Lagrangian密度$ {\ cal l} $，可保留保征不变性和电力磁性双重性，以表明dual dual到$ {\ cal l} $ is $ {\ cal l} $ is $ {\ cal k} = \ frac12 = \ frac12 \ sqrt} $} $} $} $} $} $} = sug} $} = sum} = sum} = sum {θ_其中$θ_{μν} $是由此$ {\ cal l} $构建的应力 - 能量张量。我们指出，$ {\ cal l} $和$ {\ cal k} $构成了一对典型的共轭变量，这些变量可以被视为二维符号歧管的本地坐标。
We address the lately discovered Lagrangian density ${\cal L}$ of nonlinear electrodynamics preserving both conformal invariance and electric-magnetic duality to show that the quantity dual to ${\cal L}$ is ${\cal K}=\frac12\sqrt{Θ_{μν}Θ^{μν}}$, where $Θ_{μν}$ is the stress-energy tensor built out of this ${\cal L}$. We point out that ${\cal L}$ and ${\cal K}$ make up a pair of canonically conjugate variables which can be regarded as local coordinates of a two-dimensional symplectic manifold.
