Involutive categories, colored * -operads and quantum field theory

Benini, Marco; Schenkel, Alexander; Woike, Lukas

Abstract

Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field) theory, we develop the involutive analogs of colored operads and their algebras, named colored *-operads and *-algebras. Central to the definition of colored *-operads is the involutive monoidal category of symmetric sequences, which we obtain from a general product-exponential 2-adjunction whose right adjoint forms involutive functor categories. For *-algebras over *-operads we obtain involutive analogs of the usual change of color and operad adjunctions. As an application, we turn the colored operads for algebraic quantum field theory into colored *-operads. The simplest instance is the associative *-operad, whose *-algebras are unital and associative *-algebras.

Citation

Benini, M., Schenkel, A., & Woike, L. (2019). Involutive categories, colored * -operads and quantum field theory. Theory and Applications of Categories, 34(2), 13-57

• Journal Article Type: Article
• Acceptance Date: Jan 11, 2019
• Online Publication Date: Feb 11, 2019
• Publication Date: Feb 11, 2019
• Deposit Date: Feb 12, 2019
• Publicly Available Date: Feb 12, 2019
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 2
• Pages: 13-57
• Keywords: involutive categories, involutive monoidal categories, * -monoids, colored operads,; * -algebras, algebraic quantum field theory; MSC 2010: 18Dxx, 81Txx
• Public URL: https://nottingham-repository.worktribe.com/output/1541269
• Publisher URL: http://www.tac.mta.ca/tac/volumes/34/2/34-02abs.html