Related papers: A Refined Difference Field Theory for Symbolic Sum…
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this…
We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
We present an algorithm, HOMER, for exploration and reinforcement learning in rich observation environments that are summarizable by an unknown latent state space. The algorithm interleaves representation learning to identify a new notion…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
We introduce a compressed representation of sets of sets that exploits how much they differ from each other. Our representation supports access, membership, predecessor and successor queries on the sets within logarithmic time. In addition,…
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…
Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in…
We review a performance of Fock space methods in calculating spectra of a range of supersymmetric models with gauge symmetry. Examples include: a) SU(2) Supersymmetric Yang Mills Quantum Mechanics in four euclidean dimensions, b) Quantum…
In this paper we present a novel technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. In order to extract…
This paper introduces an information-theoretic framework for text summarization. We define the summarizer rate-distortion function and show that it provides a fundamental lower bound on summarizer performance. We describe an iterative…
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…
Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This…
We give an overview of state-of-the-art multi-loop Feynman diagram computations, and explain how we use symbolic manipulation to generate renormalized integrals that are then evaluated numerically. We explain how we automate BPHZ…
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…
We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…
We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over ${\mathbb Z}_p$ can…