标题： 一种量子引力中的精确费米子陈-西蒙斯- Kodama态 显示英文标题

标题： An Exact Fermionic Chern-Simons-Kodama State in Quantum Gravity

摘要： 陈-西蒙斯-科达马（CSK）态是在爱什特克尔形式下的经典广义相对论中的一个精确的非微扰波函数。 在本工作中，我们通过精确求解 Wheeler-DeWitt 方程的扩展引力和费米子哈密顿约束，找到了一种广义的费米子 CSK 态。 我们证明，当对称性约化到 FRW 坐标并考虑微扰费米子修正时，这种新态会退化为原始的科达马态，从而与宇宙学中的哈特尔-霍金和维伦金宇宙波函数建立联系。 我们还发现，当扭率和费米子都不为零时，波函数具有有限的振幅以逃避大爆炸曲率奇点。 显示英文摘要

摘要： The Chern-Simons-Kodama (CSK) state is an exact, non-perturbative wave function in the Ashtekar formulation of classical General Relativity. In this work, we find a generalized fermionic CSK state by solving the extended gravitational and fermionic Hamiltonian constraints of the Wheeler-DeWitt equation exactly. We show that this new state reduces to the original Kodama state upon symmetry reduction to FRW coordinates with perturbative fermionic corrections, making contact with the Hartle-Hawking and Vilenkin wave functions of the universe in cosmology. We also find that when both torsion and fermions are non-vanishing, the wave function possesses a finite amplitude to evade the Big Bang curvature singularity.