Non-abelian bosonization without Wess-Zumino terms. I. New current algebra
Non-abelian bosonization without Wess-Zumino terms. I. New current algebra
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没有韦斯-祖米诺项的非阿贝尔玻色化。
DOI：
10.1016/0370-2693(89)91528-1
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发表时间：
1989
影响因子：
4.4
通讯作者：
S. Rajeev
中科院分区：
文献类型：
--
作者：
S. Rajeev
证明了不含Wess-Zumino项的非线性σ模型作为量子理论等价于非交换的无质量Thirring模型。然而，非线性模型的标准（Sugawara）电流代数与费米子理论的电流代数并不同构。提出了一种新的电流代数形式，它依赖于一个参数k。当k→∞时，它简化为Sugawara形式主义。新的流代数与费米子代数同构，是两个中心项相反的Kaplan-Moody代数的直和。在量子理论中，k（这是能级数）必须是一个整数。新的形式主义是保持庞加莱和共形不变性经典。正则地导出了新的电流代数，并提出了一种新的非线性模型作用原理。
It is conjectured that the non-linear sigma-model without Wess-Zumino terms is equivalent as a quantum theory to the non-abelian massless Thirring model. However, the standard (Sugawara) current algebra of the non-linear model is not isomorphic to that of the fermionic theory. A new current algebra formalism is proposed, which depends on a parameter k. As k→∞ it reduces to the Sugawara formalism. The new current algebra is isomorphic to the fermionic one, being the direct sum of two Kač-Moody algebras with opposite central terms. In the quantum theory, k(which is the level number) has to be an integer. The new formalism is shown to preserve Poincaré and conformal invariance classically. The new current algebra is derived canonically and a new action principle for the non-linear model is proposed.