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We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R^d (NQFT). We give a detailed classification of divergent graphs in some massive NQFT…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from…
In quantum electrodynamics, optical processes are theoretically described by double-sided Feynman diagrams. This formalism is powerful in the case of molecules but proves inappropriate to account for light-matter interactions within complex…
Let $\Gamma$ be a $Q$-polynomial distance-regular graph with diameter at least $3$. Terwilliger (1993) implicitly showed that there exists a polynomial, say $T(\lambda)\in \mathbb{C}[\lambda]$, of degree $4$ depending only on the…
We construct a state model for the two-variable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in three-dimensional space.
The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of few atomically thick layers and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced…
We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental…
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit…
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued ,…
The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative…
We propose general guidelines in order to incorporate the geometrical description of gravity in quantum field theory and address the problem of UV divergences non-perturbatively. In our aproach, each virtual particle in a Feynman graph…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
In this paper, we establish the convergence of Feynman graph integrals on closed real-analytic K\"ahler manifolds and uncover the structural mechanism underlying this convergence. The key insight is that, using Getzler's rescaling…
We introduce a type of graph integrals which are holomorphic analogs of configuration space integrals. We prove their (ultraviolet) finiteness by considering a compactification of the moduli space of graphs with metrics, and study their…