论文标题
一种通过自我预科扩展的新型晶格量规理论
A New Type of Lattice Gauge Theory through Self-adjoint Extensions
论文作者
论文摘要
可以通过考虑汉密尔顿形式主义中电场运算符的可能自我伴侣扩展来获得威尔逊晶格仪理论的概括。在3D $ \ mathrm {u}（1）$量规理论的特殊情况下，这些是通过阶段$θ$进行参数的，并且以$θ= 0 $的方式回收了普通的威尔逊理论。我们考虑了$θ=π$的情况，在双重化时，它变成了交错的整数和半固有高度变量的理论。我们研究了相关对称性的断裂阶参数，从而研究了该理论的相图，该理论的证据表明，与普通理论相反，在连续限制中损坏了$ \ mathbb {z} _2 $对称性。
A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of 3D $\mathrm{U}(1)$ gauge theory these are parametrised by a phase $θ$, and the ordinary Wilson theory is recovered for $θ=0$. We consider the case $θ=π$, which, upon dualization, turns into a theory of staggered integer and half-integer height variables. We investigate order parameters for the breaking of the relevant symmetries, and thus study the phase diagram of the theory, which shows evidence of a broken $\mathbb{Z}_2$ symmetry in the continuum limit, in contrast to the ordinary theory.
