(National Academy of Sciences, 2017) Jaffe, Arthur; Liu, Zhengwei
We give an overview of our philosophy of pictures in mathematics. We emphasize a bidirectional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.
(American Institute of Physics, 2008) Jaffe, Arthur; Ritter, Gordon
We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality \(C_D \leq C_N\) between Dirichlet and Neumann covariance operators on a manifold with a reflection.
