Crossing symmetry and the crossing map

Correa da Silva R, Giorgetti L, Lechner G (2024)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024


We introduce and study the crossing map, a closed linear map of order four acting on operators on the tensor square of a given Hilbert space inspired by the crossing property of quantum field theory. This map turns out to be closely connected to Tomita-Takesaki modular theory; in particular its fixed points define endomorphisms of standard subspaces. We also explain how the crossing property is related to finite index subfactor planar algebras/Q-systems. In the latter case, the crossing map turns out to be a special case of the (unshaded) subfactor theoretical Fourier transform.

Authors with CRIS profile

Involved external institutions

How to cite


Correa da Silva, R., Giorgetti, L., & Lechner, G. (2024). Crossing symmetry and the crossing map. (Unpublished, Submitted).


Correa da Silva, Ricardo, Luca Giorgetti, and Gandalf Lechner. Crossing symmetry and the crossing map. Unpublished, Submitted. 2024.

BibTeX: Download