Talk:Quantum field theory

Definition of $ {\rho_{\kappa}}(\Box) $

Could someone please explain the meaning of $ {\rho_{\kappa}}(\Box) $, which occurs two displayed equations below Equation (6)? I checked the published version of Encyclopedia of Mathematics to see if the expression appears there as well, and indeed it does. However, no definition is given.

Probably, the function $\rho_{\kappa}$ applied to the d'Alembertian $\Box$. In the formula for the smoothing function $D_{\kappa,\epsilon}$ we see $\rho_{\kappa}(\langle p,p \rangle)$; and this Fourier transform diagonalizes $\Box$, turning it into multiplication by $p\mapsto\langle p,p \rangle$, right? Boris Tsirelson (talk) 16:15, 5 December 2016 (CET)

Hello Professor Tsirelson. Are you referring to the use of the Borel functional calculus to define $ {\rho_{\kappa}}(\Box) $? This would make perfect sense because $ \Box $ is a self-adjoint densely-defined operator on $ {L^{2}}(\mathbb{R}^{4}) $. Leonard Huang (talk) 19:57, 5 December 2016 (CET)

Yes, I mean it. Even though I surely cannot formulate rigorously (most of) the quantum field theory.   :-)   Boris Tsirelson (talk) 20:34, 5 December 2016 (CET)