37 citations · 111 across the 23 of their papers we have counts for
24 papers
Combinatorial QFT on graphs: first quantization formalism
Ivan Contreras, Santosh Kandel, Pavel Mnev +1
We study a combinatorial model of the quantum scalar field with polynomial potential on a graph. In the first quantization formalism, the value of a Feynman graph is given by a sum…
On Examples and Classification of Frobenius Objects in Rel
Ivan Contreras, Adele Long, Sophia Marx +1
We give some new examples of Frobenius objects in the category of sets and relations . One example is a groupoid with a twisted counit. Another example is the set of…
Defects via Factorization Algebras
Ivan Contreras, Chris Elliott, Owen Gwilliam
We provide a mathematical formulation of the idea of a defect for a field theory, in terms of the factorization algebra of observables and using the BV formalism. Our approach foll…
Laplace and Dirac Operators on Graphs
Beata Casiday, Ivan Contreras, Thomas Meyer +2
Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we i…
Frobenius objects in the category of spans
Ivan Contreras, Molly Keller, Rajan Amit Mehta
We consider Frobenius objects in the category Span, where the objects are sets and the morphisms are isomorphism classes of spans of sets. We show that such structures are in corre…
On discrete gradient vector fields and Laplacians of simplicial complexes
Ivan Contreras, Andrew R. Tawfeek
Discrete Morse theory, a cell complex-analog to smooth Morse theory, has been developed over the past few decades since its original formulation by Robin Forman in 1998. In particu…