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Involutive categories, colored * -operads and quantum field theory

Benini, Marco; Schenkel, Alexander; Woike, Lukas


Marco Benini

Lukas Woike


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.


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
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