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We develop a new geometric and systematic description of the dynamics of general lumped-element electrical circuits as first order differential equations, derivable from a Lagrangian and a Rayleigh dissipation function. Through the Faddeev-Jackiw method we identify and classify the singularities that arise in the search for Hamiltonian descriptions of general networks. The core of our solution relies on the correct identification of the reduced manifold in which the circuit state is expressible, e.g., a mix of flux and charge degrees of freedom, including the presence of compact ones. We apply our fully programmable method to obtain (canonically quantizable) Hamiltonian descriptions of nonlinear and nonreciprocal circuits which would be cumbersome\/singular if pure node-flux or loop-charge variables were used as a starting configuration space. We also propose a specific assignment of topology for the branch variables of energetic elements, that when used as input to the procedure gives results consistent with classical descriptions as well as with spectra of more involved quantum circuits. This work unifies diverse existent geometrical pictures of electrical network theory, and will prove useful, for instance, to automatize the computation of exact Hamiltonian descriptions of superconducting quantum chips.<\/jats:p>","DOI":"10.22331\/q-2024-09-09-1466","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T13:58:48Z","timestamp":1725890328000},"page":"1466","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":16,"title":["Geometrical description and Faddeev-Jackiw quantization of electrical networks"],"prefix":"10.22331","volume":"8","author":[{"given":"A.","family":"Parra-Rodriguez","sequence":"first","affiliation":[{"name":"Institut Quantique and D\u00e9partement de Physique, Universit\u00e9 de Sherbrooke, Sherbrooke, Qu\u00e9bec J1K 2R1, Canada"},{"name":"Instituto de F\u00edsica Fundamental IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain"}]},{"given":"I. 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