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Dynamical Field Inference and Supersymmetry.

Margret Westerkamp1,2, Igor Ovchinnikov3, Philipp Frank1,2

  • 1Max Planck Institute for Astrophysics, Karl-Schwarzschildstraße 1, 85748 Garching, Germany.

Entropy (Basel, Switzerland)
|December 24, 2021
PubMed
Summary
This summary is machine-generated.

Dynamical field inference reconstructs evolving physical fields using information field theory. Supersymmetric theory of stochastics offers solutions to computational challenges, revealing fermionic corrections are vital for accurate posterior statistics.

Keywords:
chaos theoryfield inferenceinformation field theorystochastic differential equationssupersymmetric theory of stochastics

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Area of Science:

  • Physics
  • Information Theory
  • Stochastic Processes

Background:

  • Understanding evolving physical fields is crucial across science, technology, and economics.
  • Dynamical field inference (DFI) reconstructs dynamic fields from limited data, utilizing information field theory (IFT).
  • Challenges arise in IFT's path integral calculations due to functional Dirac functions and determinants.

Purpose of the Study:

  • To elucidate the relationships between DFI, IFT, and the supersymmetric theory of stochastics (STS).
  • To address computational hurdles in IFT by employing STS.
  • To investigate how measurement constraints and chaotic dynamics impact DFI.

Main Methods:

  • Established pedagogical connections between DFI, IFT, and STS.
  • Utilized STS to replace problematic IFT expressions with fermionic ghost and bosonic Lagrange fields.
  • Employed Feynman diagrams to analyze a simplified system with chaotic dynamics and measurement constraints.

Main Results:

  • Identified supersymmetry in STS actions, allowing boson-fermion exchange invariance.
  • Demonstrated that field measurements break this supersymmetry.
  • Showed that spontaneous symmetry breaking leads to chaotic, less predictable system evolution.
  • Highlighted the critical role of fermionic corrections for accurate posterior statistics in DFI.

Conclusions:

  • STS provides a framework to overcome IFT's computational limitations in DFI.
  • Chaotic dynamics and measurement constraints complicate DFI, necessitating advanced methods.
  • Fermionic corrections derived from STS are essential for accurate reconstruction of dynamical fields, especially in chaotic systems.