Related papers: Inductive Approach to Loop Vertex Expansion
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse…
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\phi^3$-theory. This formalism greatly facilitates the…
We introduce real induction, a proof technique analogous to mathematical induction but applicable to statements indexed by an interval on the real line. More generally we give an inductive principle applicable in any Dedekind complete…
We consider both finite and infinite power chi expansions of $f$-divergences derived from Taylor's expansions of smooth generators, and elaborate on cases where these expansions yield closed-form formula, bounded approximations, or analytic…
The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in…
We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here,…
Advances in natural language processing have resulted in increased capabilities with respect to multiple tasks. One of the possible causes of the observed performance gains is the introduction of increasingly sophisticated text…
This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
An irreducible cohomological derivation of the Freedman-Townsend vertex in four dimensions is given.
We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to…
We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $\phi^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled…
In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
It is shown that the self inductance of a wire loop may be written as a curve integral akin to the Neumann formula for the mutual inductance of two wire loops. The only difference is that contributions where the two integration variables…