Bootstrapping Elliptic Feynman Integrals Using Schubert Analysis.

Phys Rev Lett

Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.

Published: July 2023

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this Letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain the symbol alphabet, which contains 100 logarithms as well as nine simple elliptic integrals, via a Schubert-type analysis, which we equally generalize to the elliptic case. In particular, we find a compact, one-line formula for the (2,2) coproduct of the result.

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.131.041601DOI Listing

Publication Analysis

Top Keywords

feynman integrals
12
elliptic feynman
8
symbol bootstrap
8
bootstrapping elliptic
4
integrals
4
integrals schubert
4
schubert analysis
4
symbol
4
analysis symbol
4
bootstrap proven
4

Similar Publications

We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric-isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule-Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor-liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions.

View Article and Find Full Text PDF

In this paper, we propose employing electron scattering to realize unitary quantum gates that are controlled by three qubits. Using Feynman's rules, we find an expression for the transition amplitude for scattering from an external electromagnetic source. In this context, the scattering amplitude is modeled as a unitary gate whose state can be regulated.

View Article and Find Full Text PDF

Antibiotics are currently the most used antibacterial treatment for killing bacteria. However, bacteria develop resistance when continually overexposed to antibiotics. Developing antimicrobial agents that can replace existing antibiotics is essential because antibiotic-resistant bacteria have resistance mechanisms for all current antibiotics and can promote nosocomial infections.

View Article and Find Full Text PDF

Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations.

J Chem Phys

October 2024

College of Physics and Electronic Engineering, and Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China.

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method have proven to be efficient in studying open quantum systems with bosonic environments.

View Article and Find Full Text PDF

The presence of loss mechanisms governed by empirical timescales can profoundly affect the dynamics in molecular systems, leading to changes in their spectra. However, incorporation of these effects along with the system's interaction with the thermal dissipative environments proves to be challenging. In this work, we demonstrate the possibility of utilizing the recently developed path integral Lindblad dynamics (PILD) method to study the linear spectra of molecular aggregates.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!