论文标题
麦克斯韦分子理论
Maxwell theory of fractons
论文作者
论文摘要
我们表明，分面准颗粒的主要特性可以从类似麦克斯韦的广义的麦克斯韦样作用中得出。从等级-2对称张量字段$ a_ {μν}（x）$开始，我们构建了一个部分对称的rank-3张量球场强度$ f_ {μνρ}（x）$，它遵守一种比安奇身份。协变``fracton''转换下的最通用的动作不变性$Δ_{fract} a_ {μν}（x）= \partial_μ\partial_νλ（x）$组成两个独立术语：一个描述线性重力（LG）和其他可引用的术语。可以用$ f_ {μνρ}（x）$编写整个动作，而不变的拉格朗日的fracton部分则以$ f^2（x）$的形式写成，类似于麦克斯韦理论。源自面条拉格朗日的规范势头与出现在分面文献中的张量电场以及具有与协方差的麦克斯韦方程相同的磁场方程（$ \ \ partial^μf_{αβμ}（αβμ}（x）（x）= 0 $），可以和综合的电气和磁场上的均可编写，并在概括性上写下。 AmpèreLaws），而其他两个（广义的磁性高斯和法拉第法律）是Maxwell理论中的Tensor $ f_ {μνρ}（x）$的``bianchi身份''的后果。在法族人理论的协变概括中，描述了fracton有限迁移率的方程式，即$ $ the Charge and Dipole守恒，不是外部限制因素，而是运动方程的后果，因此不变性动作的后果，因此，最终是Fracton Covariant Symmetry。最后，我们通过指出两者都满足有限的迁移率特性的普遍限制，从而增加了LG和Fracton理论之间已知的类比，这在LG中不会期望。
We show that the main properties of the fracton quasiparticles can be derived from a generalized covariant Maxwell-like action. Starting from a rank-2 symmetric tensor field $A_{μν}(x)$, we build a partially symmetric rank-3 tensor field strength $F_{μνρ}(x)$ which obeys a kind of Bianchi identity. The most general action invariant under the covariant ``fracton'' transformation $δ_{fract}A_{μν}(x)=\partial_μ\partial_νΛ(x)$ consists of two independent terms: one describing Linearized Gravity (LG) and the other referable to fractons. The whole action can be written in terms of $F_{μνρ}(x)$, and the fracton part of the invariant Lagrangian writes as $F^2(x)$, in analogy with Maxwell theory. The canonical momentum derived from the fracton Lagrangian coincides with the tensor electric field appearing in the fracton Literature, and the field equations of motion, which have the same form as the covariant Maxwell equations ($\partial^μF_{αβμ}(x)=0$), can be written in terms of the generalized electric and magnetic fields and yield two of the four Maxwell equations (generalized electric Gauss and Ampère laws), while the other two (generalized magnetic Gauss and Faraday laws) are consequences of the ``Bianchi identity'' for the tensor $F_{μνρ}(x)$, as in Maxwell theory. In the covariant generalization of the fracton theory, the equations describing the fracton limited mobility, $i.e.$ the charge and dipole conservation, are not external constraints, but rather consequences of the field equations of motion, hence of the invariant action and, ultimately, of the fracton covariant symmetry. Finally, we increase the known analogies between LG and fracton theory by noting that both satisfy the generalized Gauss constraint which underlies the limited mobility property, which one would not expect in LG.
