Related papers: Feynman integrals and motives
Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone.…
We give a concise and pedagogical introduction to Feynman diagrams. After discussing a toy model which requires only undergraduate mathematics, we focus on relativistic quantum field theory. We review the derivation of Feynman rules from…
We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman…
We retrace an ab initio relativistic derivation of Maxwell's equations that was developed by Feynman in unpublished notes, clarifying the analogies and the differences with analogous treatments present in the literature. Unlike the latter,…
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and…
Let $G$ be a split semisimple algebraic group over a field and let $A^*$ be an oriented cohomology theory in the sense of Levine--Morel. We provide a uniform approach to the $A^*$-motives of geometrically cellular smooth projective…
We compare different approaches to quantum ontology. In particular, we discuss an interpretation of quantum mechanics that we call objective quantum field theory (OQFT), which involves retrocausal fields. Here, objective implies the…
This brief note publicizes the quantum framework for symmetry that is developed in our joint paper arXiv:2209.07471 with Greg Moore and Constantin Teleman. We include additional motivation and an application to a selection rule for line…
We employ the Stern-Gerlach experiment to highlight the basics of a minimalist, non-interpretational top-down approach to quantum foundations. Certain benefits of the here highlighted "quantum structural studies" are detected and discussed.…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
This article contributes to the discussion on the relationship between the Neyman-Rubin and the graphical frameworks for causal inference. We present specific examples of data-generating mechanisms - such as those involving undirected or…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
We consider the Pfaffian-Grassmannian equivalence from the motivic point of view. The main result is that under certain numerical conditions, both sides of the equivalence are related on the level of Chow motives. The consequences include a…
Group field theory has shown to be a promising framework to derive cosmological predictions from full quantum gravity. In this brief note, we revisit the background dynamics when interaction terms are taken into account and conclude that,…
A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…
We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety S over a field k of characteristic zero. We develop a theory of constructible effective Chow…
A concrete analysis of the general properties and numerical characteristics of different atomic and nuclear shell systems and subnuclear particles is carried out on the base of the solution scheme for an introduced in part I physical graph…
We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic…
We study the related questions: (i) when Feynman amplitudes in massless $\phi^4$ theory evaluate to multiple zeta values, and (ii) when their underlying motives are mixed Tate. More generally, by considering configurations of singular…