Bosonization of non-relativstic fermions in 2-dimensions and collective field theory
Bosonization of non-relativstic fermions in 2-dimensions and collective field theory
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二维非相对论费米子的玻色化和集体场论
DOI：
10.1088/1126-6708/2005/07/064
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发表时间：
2005
影响因子：
5.4
通讯作者：
A. Dhar
中科院分区：
文献类型：
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作者：
A. Dhar
我们重新讨论了一维空间中非相对论费米子的玻色化。我们的动机是最近由Lin，Lunin和Maldacena [13]对冒泡半BPS几何的工作。在回顾了早期的工作中的一个非对易理论的精确玻色子化，我们得出了一个行动的集体领域，生活在液滴边界的经典极限。我们的行动是明显的不变性下的边界依赖于时间的reparametrizations。我们证明，在适当的规范，经典的集体场方程意味着每个点的边界上满足汉密尔顿方程的经典粒子在适当的潜力。对于谐振子势，对于任何边界轮廓都可以精确地进行该作用的直接量化。对于有限个费米子，量子集体场论不能再现精确的非对易玻色化的结果，而后者与直接用费米理论计算的结果完全一致。
We revisit bosonization of non-relativistic fermions in one space dimension. Our motivation is the recent work on bubbling half-BPS geometries by Lin, Lunin and Maldacena [13]. After reviewing earlier work on exact bosonization in terms of a noncommutative theory, we derive an action for the collective field which lives on the droplet boundaries in the classical limit. Our action is manifestly invariant under time-dependent reparametrizations of the boundary. We show that, in an appropriate gauge, the classical collective field equations imply that each point on the boundary satisfies Hamilton's equations for a classical particle in the appropriate potential. For the harmonic oscillator potential, a straightforward quantization of this action can be carried out exactly for any boundary profile. For a finite number of fermions, the quantum collective field theory does not reproduce the results of the exact noncommutative bosonization, while the latter are in complete agreement with the results computed directly in the fermi theory.
冒泡 1/2 BPS 几何和彭罗斯极限
DOI：
--
发表时间：
2005
期刊：
Physical Review D 72
影响因子：
--
作者：
高山 靖敏;吉田 健太郎
通讯作者：
吉田 健太郎