Related papers: Causality and loop-tree duality at higher loops
In order to use the Gaussian representation for propagators in Feynman amplitudes, a representation which is useful to relate string theory and field theory, one has to prove first that each $\alpha$- parameter (where $\alpha$ is the…
We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(\phi^3)$ amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that…
In causal set theory the gravitational path integral is replaced by a path-sum over a sample space $\Omega_n$ of $n$-element causal sets. The contribution from non-manifold-like orders dominates $\Omega_n$ for large $n$ and therefore must…
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate…
We investigate the relation between degree sequences of trees and the majorization order using the Muirhead theorem. In this way, we prove a theorem that provides a necessary and sufficient condition for delta sequences of trees to be…
The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties.…
We consider two type of systems, a linear singular discrete time system and a linear singular fractional discrete time system whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space…
We consider two different definitions for loop corrections to the primordial power spectra. One of these is to simply correct the mode functions in the tree order relations using the linearized effective field equations. The second…
We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up…
Defant found that the relationship between a sequence of (univariate) classical cumulants and the corresponding sequence of (univariate) free cumulants can be described combinatorially in terms of families of binary plane trees called…
Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…
I prove that classical gravity coupled with quantized matter can be renormalized with a finite number of independent couplings, plus field redefinitions, without introducing higher-derivative kinetic terms in the gravitational sector, but…
In this work we define and study the relations between Lorentzian Manifolds given by the diffeomorphisms which map causal future directed vectors onto causal future directed vectors. This class of diffeomorphisms, called proper causal…
We study quantum causal structures in $1+1$ $\kappa$-Minkowski space-time described by a Lorentzian Spectral Triple whose Dirac operator is built from a natural set of twisted derivations of the $\kappa$-Poincar\'e algebra. We show that the…
This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$,…
Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between…
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the…
The two primary causal dimensions of age-related disease are rate and function. Change in rate of disease development shifts the age of onset. Change in physiological function provides necessary steps in disease progression. A causal factor…
We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…
We evaluate the Wilson loop at second order in general non-covariant gauges by means of the causal principal-value prescription for the gauge- dependent poles in the gauge-boson propagator and show that the result agrees with the usual…