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Renormalization in Open Quantum Field theory I: Scalar field theory

Avinash, Chandan Jana, R. Loganayagam, Arnab Rudra

TL;DR

This work develops and analyzes an open quantum field theory based on a relativistic $\phi^3+\phi^4$ scalar theory in $d=4$, incorporating Schwinger-Keldysh real-time evolution and Lindblad-type dissipation. Using the Feynman-Vernon influence functional and the SK formalism, the authors construct the open EFT action with doubled fields and cross-couplings, derive the exact propagators and Feynman rules, and compute the complete set of one-loop beta functions for masses and couplings, including the Lindblad-violating terms. A key result is that the one-loop renormalization preserves the Lindblad structure: the beta functions of the Lindblad-violating combinations are proportional to those combinations themselves, so starting at a Lindblad-compatible point remains closed under RG flow. An exact, all-order argument in the average-difference basis shows that perturbative corrections cannot generate pure-average Lindblad-violating vertices from a theory with none at tree level, reinforcing the robustness of the Lindblad constraints. The findings illuminate how open quantum field theories renormalise and suggest a controlled path toward open EFTs in higher-spin, gauge, or supersymmetric settings with potential applications to non-unitary dynamics in cosmology and quantum gravity.

Abstract

While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available to deal with open quantum field theories, we go on to apply these tools to an open version of $φ^3$ + $φ^4$ theory in four spacetime dimensions and demonstrate its one loop renormalizability (including the renormalizability of the Lindblad structure).

Renormalization in Open Quantum Field theory I: Scalar field theory

TL;DR

This work develops and analyzes an open quantum field theory based on a relativistic scalar theory in , incorporating Schwinger-Keldysh real-time evolution and Lindblad-type dissipation. Using the Feynman-Vernon influence functional and the SK formalism, the authors construct the open EFT action with doubled fields and cross-couplings, derive the exact propagators and Feynman rules, and compute the complete set of one-loop beta functions for masses and couplings, including the Lindblad-violating terms. A key result is that the one-loop renormalization preserves the Lindblad structure: the beta functions of the Lindblad-violating combinations are proportional to those combinations themselves, so starting at a Lindblad-compatible point remains closed under RG flow. An exact, all-order argument in the average-difference basis shows that perturbative corrections cannot generate pure-average Lindblad-violating vertices from a theory with none at tree level, reinforcing the robustness of the Lindblad constraints. The findings illuminate how open quantum field theories renormalise and suggest a controlled path toward open EFTs in higher-spin, gauge, or supersymmetric settings with potential applications to non-unitary dynamics in cosmology and quantum gravity.

Abstract

While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available to deal with open quantum field theories, we go on to apply these tools to an open version of + theory in four spacetime dimensions and demonstrate its one loop renormalizability (including the renormalizability of the Lindblad structure).

Paper Structure

This paper contains 78 sections, 208 equations, 36 figures, 2 tables.

Table of Contents

  1. Introduction and Motivation
  2. Organization of the paper
  3. Basics of Schwinger-Keldysh theory
  4. Basics of Lindblad theory and Effective theory
  5. Introduction to Open effective theory
  6. Lindblad condition
  7. Exact propagators
  8. Feynman rules
  9. Lindblad condition from tree level correlators
  10. One loop beta function
  11. One loop beta function for m squared
  12. One loop beta function for mdelta
  13. Checking Lindblad condition for mass renormalization
  14. One loop beta function for L3
  15. One loop beta function for sigma3
  16. ...and 63 more sections

Figures (36)

  • Figure 1: Feynman-Vernon vertex of an open QFT
  • Figure 2: SK propagator for $\phi$ fields
  • Figure 3: Diagrammatic Representation of all the Tree level processes
  • Figure 4: One Loop corrections to $m^2$ due to cubic couplings
  • Figure 5: One loop correction to $m^2$ due to quartic couplings
  • ...and 31 more figures