Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf monoids, permutohedral cones, and generalized retarded functions   The commutative Hopf monoid of set compositions is a fundamental Hopf monoid
internal to vector species, having undecorated bosonic Fock space the
combinatorial Hopf algebra of quasisymmetric functions. We construct a
geometric realization of this Hopf monoid over the adjoint of the
(essentialized) braid hyperplane arrangement, which identifies the monomial
basis with signed characteristic functions of the interiors of permutohedral
tangent cones. We show that the indecomposable quotient Lie coalgebra is
obtained by restricting functions to chambers of the adjoint arrangement, i.e.
by quotienting out the higher codimensions. The resulting functions are
characterized by the Steinmann relations of axiomatic quantum field theory,
demonstrating an equivalence between the Steinmann relations, tangent cones to
(generalized) permutohedra, and having algebraic structure internal to species.
Our results give a new interpretation of a construction appearing in the
mathematically rigorous formulation of renormalization by Epstein-Glaser,
called causal perturbation theory. In particular, we show that operator
products of time-ordered products correspond to the H-basis of the
cocommutative Hopf monoid of set compositions, and generalized retarded
products correspond to a spanning set of its primitive part Lie algebra.

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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg