Crossing symmetry and the crossing map

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

Publication Language: English

Publication Status: Accepted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2024

Journal

Reviews in Mathematical Physics World Scientific Publishing

DOI: 10.1142/S0129055X24610051

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) (Heisenberg-Professur)

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. Reviews in Mathematical Physics. https://doi.org/10.1142/S0129055X24610051

MLA:

Correa da Silva, Ricardo, Luca Giorgetti, and Gandalf Lechner. "Crossing symmetry and the crossing map." Reviews in Mathematical Physics (2024).

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