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arXiv 0810.0188hep-th
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(A)dS背景上的自旋粒子和高自旋场

Spinning particles and higher spin fields on (A)dS backgrounds

Fiorenzo Bastianelli, Olindo Corradini, Emanuele Latini

摘要:

自旋粒子模型可以用来描述一次量子化中的高自旋场。在本文中,我们讨论如何自旋粒子与规范O(N)超对称的世界线可以始终耦合到共形平坦的时空,在经典和量子水平。特别地,我们考虑平坦和(A)dS背景下的正则量子化,并详细讨论了由于世界线规范对称性的约束如何产生更高自旋场的几何方程,即用广义曲率表示的方程。在平坦空间上,约束代数是线性的,并且可以通过引入规范势来积分部分约束。这样,几何公式与标准公式在规范势方面的等价性就得到了证明。在(A)dS背景下,约束代数变成二次的,然而人们可以用它来扩展以前对这种情况的分析。特别地,我们推导出了用规范势表示曲率的一般公式,并明确地讨论了自旋为2、3和4的情况。

英文摘要:

Spinning particle models can be used to describe higher spin fields in first quantization. In this paper we discuss how spinning particles with gauged O(N) supersymmetries on the worldline can be consistently coupled to conformally flat spacetimes, both at the classical and at the quantum level. In particular, we consider canonical quantization on flat and on (A)dS backgrounds, and discuss in detail how the constraints due to the worldline gauge symmetries produce geometrical equations for higher spin fields, i.e. equations written in terms of generalized curvatures. On flat space the algebra of constraints is linear, and one can integrate part of the constraints by introducing gauge potentials. This way the equivalence of the geometrical formulation with the standard formulation in terms of gauge potentials is made manifest. On (A)dS backgrounds the algebra of constraints becomes quadratic, nevertheless one can use it to extend much of the previous analysis to this case. In particular, we derive general formulas for expressing the curvatures in terms of gauge potentials and discuss explicitly the cases of spin 2, 3 and 4.

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