Constructs motivic local systems for one-loop graphs in momentum space whose weight-graded pieces are Tate twists of quadratic Artin motives from maximally cut quotient graphs, along with a formula for the de Rham motivic Galois group action.
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A dedicated global model structure for K-linear ∞-local systems is constructed via simplicial chain complexes, monoidal for base 1-types under the external tensor product.
The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.
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Motivic Galois theory for one-loop Feynman integrals in momentum space
Constructs motivic local systems for one-loop graphs in momentum space whose weight-graded pieces are Tate twists of quadratic Artin motives from maximally cut quotient graphs, along with a formula for the de Rham motivic Galois group action.
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A Global Model Structure for $\mathbb{K}$-Linear $\infty$-Local Systems
A dedicated global model structure for K-linear ∞-local systems is constructed via simplicial chain complexes, monoidal for base 1-types under the external tensor product.
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A construction of the polylogarithm motive
The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
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Entanglement of Sections: The pushout of entangled and parameterized quantum information
The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.