Conserved and nonconserved Noether currents from the quantum effective action
Abstract
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.
- Publication Date:
- Research Org.:
- Florida State Univ., Tallahassee, FL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1864895
- Alternate Identifier(s):
- OSTI ID: 1980070
- Grant/Contract Number:
- FG-02-08ER41450; FG02-06ER41450; SFB 1225
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 105 Journal Issue: 8; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Physics; functional renormalization group; symmetries
Citation Formats
Floerchinger, Stefan, and Grossi, Eduardo. Conserved and nonconserved Noether currents from the quantum effective action. United States: N. p., 2022.
Web. doi:10.1103/PhysRevD.105.085015.
Floerchinger, Stefan, & Grossi, Eduardo. Conserved and nonconserved Noether currents from the quantum effective action. United States. https://doi.org/10.1103/PhysRevD.105.085015
Floerchinger, Stefan, and Grossi, Eduardo. Mon .
"Conserved and nonconserved Noether currents from the quantum effective action". United States. https://doi.org/10.1103/PhysRevD.105.085015.
@article{osti_1864895,
title = {Conserved and nonconserved Noether currents from the quantum effective action},
author = {Floerchinger, Stefan and Grossi, Eduardo},
abstractNote = {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.},
doi = {10.1103/PhysRevD.105.085015},
journal = {Physical Review D},
number = 8,
volume = 105,
place = {United States},
year = {2022},
month = {4}
}
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