Conserved and nonconserved Noether currents from the quantum effective action

Floerchinger, Stefan; Grossi, Eduardo

doi:10.1103/physrevd.105.085015

Title: Conserved and nonconserved Noether currents from the quantum effective action

Journal Article · 25 April 2022 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.105.085015 · OSTI ID:1864895

^[1]; Grossi, Eduardo ^[2]

Friedrich Schiller Univ., Jena (Germany); Ruprecht Karls Univ., Heidelberg (Germany)
Stony Brook Univ., NY (United States)

The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be generalized beyond the standard symmetry transformations that leave the action invariant. We also discuss an extended set of transformations, which change the action by a term that is locally known on the level of the quantum effective action. Associated to such extended gauge transformations are currents for which we obtain a divergence-type equation of motion, but they are not conserved. We call them nonconserved Noether currents. We discuss, in particular, symmetries and extended transformations associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations, and local shear transformations. Together they constitute the symmetry group of the frame bundle GL(d). The corresponding nonconserved Noether currents are the dilatation or Weyl current, the spin current, and the shear current. In particular, for the latter, we obtain a new divergence-type equation of motion.

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Research Organization:: Florida State Univ., Tallahassee, FL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-06ER41450; SFB 1225; FG-02-08ER41450

OSTI ID:: 1864895

Alternate ID(s):: OSTI ID: 1980070

Journal Information:: Physical Review. D., Vol. 105, Issue 8; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Conserved and nonconserved Noether currents from the quantum effective action

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