37 citations · 111 across the 23 of their papers we have counts for
14 papers · 1 filter
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…
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…
Convolution algebras for Relational Groupoids and Reduction
Ivan Contreras, Nima Moshayedi, Konstantin Wernli
We introduce the notions of relational groupoids and relational convolution algebras. We provide various examples arising from the group algebra of a group and a given normal s…
Poly-symplectic Geometry and the AKSZ Formalism
Ivan Contreras, Nicolas Martinez Alba
We extend the AKSZ formulation of the Poisson sigma model to more general target spaces, and we develop the general theory of graded geometry for poly-symplectic and poly-Poisson s…
Gluing of Graph Laplacians and Their Spectra
Ivan Contreras, Michael Toriyama, Chengzheng Yu
We study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges t…
Kähler fibrations in quantum information theory
Ivan Contreras, Michele Schiavina
We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible Kähler structure. The case of the unitary group allows us to reformulate…
Hyperwalk Formulae for Even and Odd Laplacians in Finite CW-Hypergraphs
Ivan Contreras, Sarah Loeb, Chengzheng Yu
In this note we provide a combinatorial interpretation for the powers of the hypergraph Laplacians. Our motivation comes from the discrete formulation of quantum mechanics and ther…
Poly-Poisson Sigma models and their relational poly-symplectic groupoids
Ivan Contreras, Nicolás Martínez Alba
The main idea of this note is to describe the integration procedure for poly-Poisson structures, that is, to find a poly-symplectic groupoid integrating a poly-Poisson structure, i…
A Functorial Construction of Quantum Subtheories
Ivan Contreras, Ali Nabi Duman
We apply the geometric quantization procedure via symplectic groupoids proposed by E. Hawkins to the setting of epistemically restricted toy theories formalized by Spekkens. In the…
The Graph Laplacian and Morse Inequalities
Ivan Contreras, Boyan Xu
The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted…
Geometric Quantization and Epistemically Restricted Theories: The Continuous Case
Ivan Contreras, Ali Nabi Duman
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have ab…
On the geometry of mixed states and the Fisher information tensor
Ivan Contreras, Elisa Ercolessi, Michele Schiavina
In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher inform…
Groupoids, Frobenius algebras and Poisson sigma models
Ivan Contreras
In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between…