具有自旋结构流形上的经典Chern-Simons
Classical Chern-Simons on manifolds with spin structure
摘要：
我们在具有自旋结构的流形上构造了一个2+1维经典规范理论，它的作用量是扭曲Dirac算子的Atiyah-Patodi- Singer η-不变量的一个改进.本文研究了闭旋3-流形和紧旋3-流形的拉格朗日域论的性质，其中作用被解释为扭曲Dirac算子的Pfronan线的幺正元。然后，我们研究了形式为（R x Y）的3-流形上的哈密顿域论的性质，其中Y是一个封闭的自旋2-流形。由作用量导出了Y上平坦规范场模堆上的幺正线丛。
英文摘要：
We construct a 2+1 dimensional classical gauge theory on manifolds with spin structure whose action is a refinement of the Atiyah-Patodi- Singer eta-invariant for twisted Dirac operators. We investigate the properties of the Lagrangian field theory for closed, spun 3-manifolds and compact, spun 3-manifolds with boundary where the action is interpreted as a unitary element of a Pfaffian line of twisted Dirac operators. We then investigate the properties of the Hamiltonian field theory over 3-manifolds of the form (R x Y), where Y is a closed, spun 2-manifold. From the action we derive a unitary line bundle with connection over the moduli stack of flat gauge fields on Y.
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