Published 2019 | Version v1
Journal article Metadata-only

Harmonic analysis and mean field theory

Creators

  • 1. Institute of Physics (EPFL), Lausanne (Switzerland)
  • 2. Institute for Advanced Study, Princeton, NJ (United States)
  • 3. California Institute of Technology (CalTech), Pasadena, CA (United States)

Description

We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. As an application, we give a general formula for OPE coefficients in Mean Field Theory (MFT) for arbitrary spinning operators. We apply this formula to several examples, including MFT for fermions and "seed" operators in 4d, and MFT for currents and stress-tensors in 3d.

Availability note (English)

Available from https://www.osti.gov/servlets/purl/1594253; https://www.osti.gov/biblio/1594253; DOE Accepted Manuscript full text, or the publishers Best Available Version will be available free of charge after the embargo period

Additional details

Identifiers

URL
https://www.osti.gov/servlets/purl/1594253; https://www.osti.gov/biblio/1594253;
DOI
10.1007/JHEP10(2019)217;

Publishing Information

Journal Title
Journal of High Energy Physics (Online)
Journal Volume
2019
Journal Issue
10
Journal Page Range
vp.
ISSN
1029-8479

INIS

Country of Publication
Germany
Country of Input or Organization
United States
INIS RN
54046603
Subject category
S72: PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
Descriptors DEI
CONFORMAL GROUPS; CONFORMAL INVARIANCE; EUCLIDEAN SPACE; FIELD OPERATORS; HARMONICS; MEAN-FIELD THEORY; QUANTUM FIELD THEORY; THREE-DIMENSIONAL CALCULATIONS
Descriptors DEC
FIELD THEORIES; INVARIANCE PRINCIPLES; LIE GROUPS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; OSCILLATIONS; QUANTUM OPERATORS; RIEMANN SPACE; SPACE; SYMMETRY GROUPS

Optional Information

Contract/Grant/Project number
SC0019085; SC0009988
Funding organization
USDOE Office of Science - SC, High Energy Physics (HEP) (United States); Swiss National Science Foundation (SNF) (Switzerland)
Secondary number(s)
OSTIID--1594253