arXiv 1208.31752012-08hep-th

涡旋Lorentz对称性的自发破缺与顶点算符

Spontaneous Breaking of Lorentz Symmetry and Vertex Operators for Vortices

A. P. Balachandran, Seckin Kurkcuoglu, Amilcar R. de Queiroz

备注：: Published version, 15+1 pages, 1 figure
发表信息：: Mod. Phys. Lett. A, Vol. 28, No. 8 (2013) 1350028
DOI：: 10.1142/S0217732313500284

摘要：

本文首先回顾了无质量规范场和亚粒子存在下的自发洛伦兹对称性破缺。这个结果是很久以前在Frohlich等人严格的量子场论中得到的。和重新制定的Balachandran和Vaidya使用的概念，超选择部门和方向相关的测试功能，在空间无穷远的非本地可观的。受这些发展的启发，并在假设电荷的频谱是量子化的情况下，（以基本电荷e为单位），我们构造了一个顶点算子族，该顶点算子族创建缠绕数k，从真空（零缠绕数扇区）带电阿贝尔涡旋和/或将缠绕数移位k个单位。特别地，我们发现对于旋转涡旋，在U（1）规范场作用下，顶点算符使涡旋的角动量移动k \frac{\tilde q}{q}，其中\tilde q是涡旋量子态的电荷，q是涡旋标量场的电荷.我们还表明，对于带电粒子-涡旋复合物，角动量本征值移动了k \frac{\tilde q}{q}，{ \tilde q}是带电粒子-涡旋复合物的电荷。这导致的结果是，对于\frac{\tilde q}{q}半奇积分和奇k我们的顶点运营商翻转的统计带电粒子涡旋复合从玻色子费米子，反之亦然。对于\frac{\tilde q}{q}的分数值，顶点算符在带电粒子-涡旋复合体上的应用一般导致具有任意子统计的复合体。

英文摘要：

We first review the spontaneous Lorentz symmetry breaking in the presence of massless gauge fields and infraparticles. This result was obtained long time ago in the context of rigorious quantum field theory by Frohlich et. al. and reformulated by Balachandran and Vaidya using the notion of superselection sectors and direction-dependent test functions at spatial infinity for the non-local observables. Inspired by these developments and under the assumption that the spectrum of the electric charge is quantized, (in units of a fundamental charge e) we construct a family of vertex operators which create winding number k, electrically charged Abelian vortices from the vacuum (zero winding number sector) and/or shift the winding number by k units. In particular, we find that for rotating vortices the vertex operator at level k shifts the angular momentum of the vortex by k \frac{\tilde q}{q}, where \tilde q is the electric charge of the quantum state of the vortex and q is the charge of the vortex scalar field under the U(1) gauge field. We also show that, for charged-particle-vortex composites angular momentum eigenvalues shift by k \frac{\tilde q}{q}, {\tilde q} being the electric charge of the charged-particle-vortex composite. This leads to the result that for \frac{\tilde q}{q} half-odd integral and for odd k our vertex operators flip the statistics of charged-particle-vortex composites from bosons to fermions and vice versa. For fractional values of \frac{\tilde q}{q}, application of vertex operator on charged-particle-vortex composite leads in general to composites with anyonic statistics.

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