2024/01/24 by Alberto Ibort, Ibort, A., Macarena Jiménez-Vázquez +1 · 1 citation
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2401.13763
openalex publication_date 2024/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A Lagrangian description of the qubit based on a generalization of Schwinger's picture of Quantum Mechanics using the notion of groupoids is presented. In this formalism a Feynman-like computation of its probability amplitudes is done. The Lagrangian is interpreted as a function on the groupoid describing the quantum system. Such Lagrangian determines a self-adjoint element on its associated algebra. Feynman's paths are replaced by histories on the groupoid which form themselves a groupoid. A simple method to compute the sum over all histories is discussed. The unitarity of the propagator obtained in this way imposes quantization conditions on the Lagrangian of the theory. Some particular instances of them are discussed in detail.