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  • Open Access

Quantum tunneling in the presence of Noether charges

Giulio Barni1,* and Thomas Steingasser1,2,†

  • *Contact author: giulio.barni@ift.csic.es
  • †Contact author: thomas.steingasser@uam.es
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Phys. Rev. D 114, 056003 – Published 2 September, 2026

DOI: https://doi.org/10.1103/b3z7-t8m9

Abstract

We provide a complete first-principles based discussion of quantum tunneling out of initial states carrying a conserved Noether charge. Our main result is a simple, unambiguous Euclidean-time prescription for the calculation of tunneling rates out of such states. By relying on a combination of the direct approach and the steadyon framework for the evaluation of real-time path integrals, our derivation offers full transparency of its underlying assumptions, and is independent of any ad hoc generalizations. This strategy also offers a simple explanation for the emergence of complex saddle points for such systems, justifying techniques postulated by earlier works. Our analysis furthermore offers the first results for initial states with both a conserved Noether charge and a nontrivial energy. We first illustrate the main conceptual points of our analysis for the simple example of a point particle in two spatial dimensions carrying a conserved angular momentum. Then, we generalize our results to the case of multiple dimensions and an arbitrary conserved Noether charge, providing an easy-to-implement prescription for the calculation of the tunneling rate. We furthermore apply our results to the example of a complex scalar field subject to a global U(1)-symmetry with associated charge. These results provide a reliable foundation for the calculation of tunneling rates in applications in finite-density and charge-asymmetric systems.

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Phys. Rev. D 114, 056003– Published 2 September, 2026
  • Received 20 April 2026
  • Accepted 4 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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