格点场论中的可观测电流
Observable currents in lattice field theories
摘要：
可观测流是时空局部对象，当它们在辅助余维1表面上积分时，会产生物理可观测量。由于所得到的观测量与积分表面的局部变形无关，因此电流本身携带了有关感应物理观测量的大部分信息。我介绍了可观察到的电流在离散时空的拉格朗日场论的多辛框架。其中一个例子是由诺特电流组成的。一个更大的例子家族是由电流、时空局部对象组成的，它们对两个与解空间相切的任意向量之间的辛积进行编码。一个弱版本的可观测电流，这在一般情况下是非本地的，也介绍了。弱的可观测电流可以用来分离物理上不同的解空间中的点。结果表明，一大类弱可观测电流可以“改善”成为本地。泊松括号给出了可观测电流的空间的李代数的结构。Peierls括号体观测给出了一个代数同态映射的等价类体观测到弱可观测电流。这项研究涵盖了标量场，非线性西格玛模型和规范理论（包括规范理论公式的广义相对论）的晶格。即使本文是完全经典的，这项研究是相关的量子场论，因为量子化的框架导致自旋泡沫模型制定的晶格场论。
英文摘要：
Observable currents are spacetime local objects that induce physical observables when integrated on an auxiliary codimension one surface. Since the resulting observables are independent of local deformations of the integration surface, the currents themselves carry most of the information about the induced physical observables. I introduce observable currents in a multisymplectic framework for Lagrangian field theory over discrete spacetime. One family of examples is composed by Noether currents. A much larger family of examples is composed by currents, spacetime local objects, that encode the symplectic product between two arbitrary vectors tangent to the space of solutions. A weak version of observable currents, which in general are nonlocal, is also introduced. Weak observable currents can be used to separate points in the space of physically distinct solutions. It is shown that a large class of weak observable currents can be "improved" to become local. A Poisson bracket gives the space of observable currents the structure of a Lie algebra. Peierls bracket for bulk observables gives an algebra homomorphism mapping equivalence classes of bulk observables to weak observable currents. The study covers scalar fields, nonlinear sigma models and gauge theories (including gauge theory formulations of general relativity) on the lattice. Even when this paper is entirely classical, this study is relevant for quantum field theory because a quantization of the framework leads to a spin foam model formulation of lattice field theory.
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