Padé approximants and analytic continuation of Euclidean Φ-derivable approximations

Padé approximants and analytic continuation of Euclidean Φ-derivable approximations We investigate the Padé approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second Riemann sheet. We test this method using various benchmarks at zero temperature: a simple perturbative approximation as well as the two-loop Φ-derivable approximation. The analytic continuation method is then applied to Euclidean data previously obtained in the O(4) symmetric model (within a given renormalization scheme) to assess the difference between zero-momentum and pole masses, which is in general a difficult question to answer within nonperturbative approaches such as the Φ-derivable expansion scheme. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Padé approximants and analytic continuation of Euclidean Φ-derivable approximations

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Padé approximants and analytic continuation of Euclidean Φ-derivable approximations

Abstract

We investigate the Padé approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second Riemann sheet. We test this method using various benchmarks at zero temperature: a simple perturbative approximation as well as the two-loop Φ-derivable approximation. The analytic continuation method is then applied to Euclidean data previously obtained in the O(4) symmetric model (within a given renormalization scheme) to assess the difference between zero-momentum and pole masses, which is in general a difficult question to answer within nonperturbative approaches such as the Φ-derivable expansion scheme.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.036002
Publisher site
See Article on Publisher Site

Abstract

We investigate the Padé approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second Riemann sheet. We test this method using various benchmarks at zero temperature: a simple perturbative approximation as well as the two-loop Φ-derivable approximation. The analytic continuation method is then applied to Euclidean data previously obtained in the O(4) symmetric model (within a given renormalization scheme) to assess the difference between zero-momentum and pole masses, which is in general a difficult question to answer within nonperturbative approaches such as the Φ-derivable expansion scheme.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Aug 1, 2017

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