Title: Hamiltonians for Two-Anyon Systems Show Chinese title

Title: 两个任意子系统的哈密顿量

Abstract: We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schr\"odinger operator. We finally extend the results in presence of a two-body radial interaction. Show Chinese abstract

Abstract: 我们研究在磁规范下两个任意子系统哈密顿量的适定性。 我们确定所有可能实现该算子的二次形式，适用于非相互作用的任意子，并证明它们的闭性和下界性。 然后我们表明，相应的自伴算子会生成一个一参数的扩展族，这些扩展是朴素的两任意子薛定谔算子的扩展。 最后，我们在存在两体径向相互作用的情况下扩展了这些结果。