Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space. In particular, we study the Coulomb gauge and observe that the naive gauge potential degrees of freedom cease to be local operators as soon as we impose the Dirac brackets. We construct new local set of operators and compute the entanglement entropy according to this algebra in $2+1$ dimensions. We find that our proposal would lead to an entanglement entropy that behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers. We explore also the situation where the gauge field is Higgsed, and construct a local operator algebra that again requires some deformation. This should give us some insight into interpreting the entanglement entropy in generic gauge theories and perhaps also in gravitational theories.Comment: 38 pages,25 figure

Surgical treatment of neuropathic pain

Neuropathic pain (NP) is a transient dysfunction caused by the damage of peripheral nerve and central nervous system, characterized with hyperalgesia, allodynia and spontaneous pain. Surgical treatment of neuropathic pain has experienced a long process, and plays an important role. This paper reviews recent documents of surgical techniques in the treatment of neuropathic pain. There are three kinds of surgical techniques: neuromodulation, microsurgical lesions and nerve decompression