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Publication Type: Unpublished / Preprint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

Abstract

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

Ricardo Correa da Silva Lehrstuhl für Mathematik (Algebra und Geometrie) Gandalf Lechner Lehrstuhl für Mathematik (Operatoralgebren)

Involved external institutions

Università degli Studi di Roma 'Tor Vergata'

Italy (IT)

How to cite

APA:

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 (Unpublished, Submitted).

MLA:

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 Unpublished, Submitted. 2024.

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