Geodesic
Involutive categories, colored *-operads and quantum field theory
Theory and applications of categories, Tome 34 (2019), pp. 13-57

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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.

Publié le :
Classification : 18Dxx, 81Txx
Keywords: involutive categories, involutive monoidal categories, *-monoids, colored operads, *-algebras, algebraic quantum field theory 
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     title = {Involutive categories, colored *-operads and quantum field theory},
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Marco Benini; Alexander Schenkel; Lukas Woike. Involutive categories, colored *-operads and quantum field theory. Theory and applications of categories, Tome 34 (2019), pp. 13-57. http://geodesic.mathdoc.fr/item/TAC_2019_34_a1/