标题： 无任何截断的简化狄拉克相互作用算子的自伴性 显示英文标题

标题： Self-adjointness of a simplified Dirac interaction operator without any cutoffs

摘要： 我们证明了由$\hat H_\mathrm{I} \propto \int d\mathbf{k}d\mathbf{p}(\hat a(\mathbf{k}) + \hat a^\dagger(-\mathbf{k})) \hat b^\dagger(\mathbf{p} + \mathbf{k}) \hat b(\mathbf{p})/\sqrt{|\mathbf{k}|}$给出的狄拉克相互作用算子的一个简化版本在某个在希尔伯特空间中稠密的定义域上是自伴的，即使没有任何截断。 我们用于证明这一点的技术可能可以扩展到更广泛的算子范围。 因此，这项技术可能会在未来导致更数学上严格定义的量子场论理论。 显示英文摘要

摘要： We show that a simplified version of the Dirac interaction operator given by $\hat H_\mathrm{I} \propto \int d\mathbf{k}d\mathbf{p}(\hat a(\mathbf{k}) + \hat a^\dagger(-\mathbf{k})) \hat b^\dagger(\mathbf{p} + \mathbf{k}) \hat b(\mathbf{p})/\sqrt{|\mathbf{k}|}$ is self-adjoint on a certain domain that is dense in the Hilbert space, even without any cutoffs. The technique that we use for showing this can potentially be extended to a much wider range of operators as well. This technique might therefore potentially lead to more mathematically well-defined theories of QFT in the future.