论文标题
根据规格不变领域的重新制定量规理论
Reformulation of gauge theories in terms of gauge invariant fields
论文作者
论文摘要
我们从规格不变的领域进行了重新制定规定的重新制定。我们专注于阿贝里亚理论，我们表明可以重新组合量规和物质协方差领域，以引入新的规格不变级自由度。从定期和开放边界条件下的$（1+1）$尺寸案例开始，然后我们将其推广到更高的维度和连续限制。为了显示重新制定的明确和身体相关的例子，我们将其应用于（静态）磁场中的单个粒子的哈密顿量，将其应用于纯Abelian晶格理论，向$（3+1）$ dimensions的量子电动力学的拉格朗日式，并将其用于$ 2D $和2D $ 3D $ 3D $ HOFSTADTERSTADTERSTADTERSTADTERSTADTERSTADTERSTADTERSTADTERSTADTERSTADTERSTADTERSADTERSADTERSTADTERSTADTER。在后者中，我们表明，用于消除仪表协变量的特定结构进入了磁性布里渊区的定义。最后，我们简要评论了提出的重新制定与相互作用量规理论的研究的相关性。
We present a reformulation of gauge theories in terms of gauge invariant fields. Focusing on Abelian theories, we show that the gauge and matter covariant fields can be recombined to introduce new gauge invariant degrees of freedom. Starting from the $(1+1)$ dimensional case on the lattice, with both periodic and open boundary conditions, we then generalize to higher dimensions and to the continuum limit. To show explicit and physically relevant examples of the reformulation, we apply it to the Hamiltonian of a single particle in a (static) magnetic field, to pure abelian lattice gauge theories, to the Lagrangian of quantum electrodynamics in $(3+1)$ dimensions and to the Hamiltonian of the $2d$ and $3d$ Hofstadter model. In the latter, we show that the particular construction used to eliminate the the gauge covariant fields enters the definition of the magnetic Brillouin zone. Finally, we briefly comment on relevance of the presented reformulation to the study of interacting gauge theories.
