Non-equilibrium quantum field theory of the free-electron laser in Keldysh formalism

Quantum Physics arXiv:2512.05266 (quant-ph) [Submitted on 4 Dec 2025] Title:Non-equilibrium quantum field theory of the free-electron laser in Keldysh formalism Authors:Loris Di Cairano View a PDF of the paper titled Non-equilibrium quantum field theory of the free-electron laser in Keldysh formalism, by Loris Di Cairano View PDF HTML (experimental) Abstract:We develop a non-equilibrium quantum field theory of the free-electron laser based on the Preparata model, using the real-time Keldysh formalism. Starting from a microscopic Lagrangian for a relativistic electron beam coupled to a single radiation mode, we construct a Keldysh functional integral, perform the large-N rescaling, and integrate out the electronic degrees of freedom. This yields an effective action for the FEL mode in which dispersion, gain, and noise are all generated by a single electronic self-energy built from the current correlations of the beam. For a stationary Gaussian beam, we obtain closed analytic expressions for the retarded and Keldysh components of the self-energy, which directly encode frequency pulling, gain reduction due to energy spread, and the noise spectrum experienced by the field. At low frequency, the theory reduces to a Landau-Ginzburg-Keldysh description of a single complex mode with a mass, growth rate, nonlinearity, and noise strength fully determined by beam current, energy spread, and detuning. In this framework, the FEL threshold appears as a continuous non-equilibrium phase transition in the laser universality class: the coherent field amplitude plays the role of an order parameter, while the amplitude of critical fluctuations is fixed by the microscopic noise kernel. The result is a minimal open quantum field theory analog of Vlasov-Maxwell FEL theory, in which gain, dispersion, and noise arise from a unified self-energy framework rather than from separate phenomenological ingredients. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.05266 [quant-ph] (or arXiv:2512.05266v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.05266 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Loris Di Cairano [view email] [v1] Thu, 4 Dec 2025 21:40:13 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-equilibrium quantum field theory of the free-electron laser in Keldysh formalism, by Loris Di CairanoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)