Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 36 min ago
PreprintarXiv licencearXiv

A Gauge Theory of Turbulence:

  • V. E. R. Lemes
Open at sourcePDFDOICite

Abstract

We formalize the gauge structure of the Navier--Stokes equation for incompressible fluids, interpreting ∇·v=0 as a gauge fixing analogous to the Coulomb gauge in electromagnetism. We construct the Martin--Siggia--Rose action and its full BRST symmetry, introducing BRST doublets for the Gribov parameter γ and the monodromy phase θ. Through a Higgs mechanism, γ acquires a vacuum expectation value γ0, generating a mass scale for the vorticity and the ghosts; we compute the one-loop effective potential and analyze vacuum stability. Intermittency --- measured by the exponents ζn --- is described by fluctuations of the Higgs field σ around the condensate, via a Gribov-inspired log-Poisson hierarchy that satisfies exactly ζ3=1 (Kolmogorov's four-fifths law). Fits to DNS data favor filamentary vorticity structures, with Df≈1 (one parameter) or Df≈2.1, Δ≈0.44 (two parameters). The one-loop anomalous dimension in d=3, Δσ≈0.50, supports the identification Df=2Δσ. The formalism unifies classical hydrodynamics with gauge theory and spontaneous symmetry breaking, opening the study of turbulence and intermittency to quantum field theory methods.

Versions

Related

  1. Quantum computation of hadron scattering in a lattice gauge theory
    Zohreh Davoudi, Chung-Chun Hsieh, Saurabh V. Kadam
    Physical review. D/Physical review. D.Peer-reviewedLicence not statedFull text60 citedHigh-energy & particle physicsOpenAlex
  2. Probing False Vacuum Decay on a Cold-Atom Gauge-Theory Quantum Simulator
    Anonymous, Ying Liu, Gianluca Lagnese +9
    Physical Review LettersPeer-reviewedLicence not statedFull text60 citedAtomic, molecular & optical physicsOpenAlex
  3. Higher abelian gauge theory in BV formalism
    Shuhan Jiang
    arXivPreprintCC BY 4.0Full textMathematical physicsHigh-energy & particle physicsarXiv
  4. Dyonic edge modes in Abelian gauge theory
    Keito Shimizu, Sotaro Sugishita
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  5. Higher Gauge Theory via Differential Nonabelian Cohomology
    Hisham Sati, Urs Schreiber
    arXivPreprintarXiv licenceFull textGeometry & topologyMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{lemes2026gauge,
  title = {{A Gauge Theory of Turbulence:}},
  author = {V. E. R. Lemes},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05544},
  eprint = {2609.05544},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05544},
}
RIS
TY  - UNPB
TI  - A Gauge Theory of Turbulence:
AU  - V. E. R. Lemes
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.05544
UR  - https://arxiv.org/abs/2609.05544
AB  - We formalize the gauge structure of the Navier--Stokes equation for incompressible fluids, interpreting ∇·v=0 as a gauge fixing analogous to the Coulomb gauge in electromagnetism. We construct the Martin--Siggia--Rose action and its full BRST symmetry, introducing BRST doublets for the Gribov parameter γ and the monodromy phase θ. Through a Higgs mechanism, γ acquires a vacuum expectation value γ_0, generating a mass scale for the vorticity and the ghosts; we compute the one-loop effective potential and analyze vacuum stability. Intermittency --- measured by the exponents ζ_n --- is described by fluctuations of the Higgs field σ around the condensate, via a Gribov-inspired log-Poisson hierarchy that satisfies exactly ζ_3=1 (Kolmogorov's four-fifths law). Fits to DNS data favor filamentary vorticity structures, with D_f≈1 (one parameter) or D_f≈2.1, Δ≈0.44 (two parameters). The one-loop anomalous dimension in d=3, Δ_σ≈0.50, supports the identification D_f=2Δ_σ. The formalism unifies classical hydrodynamics with gauge theory and spontaneous symmetry breaking, opening the study of turbulence and intermittency to quantum field theory methods.
ER  -