https://doi.org/10.1140/epjp/s13360-024-05078-2
Regular Article
A Lagrangian path integral approach to the qubit
1
Department of Mathematics, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés, Madrid, Spain
2
ICMAT, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C. Nicolás Cabrera, 13–15, Fuencarral-El Pardo, 28049, Madrid, Spain
Received:
29
January
2024
Accepted:
8
March
2024
Published online:
3
April
2024
A Lagrangian description of the qubit based on Schwinger’s picture of Quantum Mechanics that allows for a Feynman-like computation of its probability amplitudes is presented. The Lagrangian is a function on the groupoid that describes the qubit and at the same time determines a self-adjoint element on its associated algebra. Feynman’s paths are replaced by histories on the groupoid which form a groupoid again, and a simple method to compute the sum over all histories is discussed. The unitarity of the theory described in this way imposes quantization conditions on the parameters determining the Lagrangian, and some particular instances are solved completely.
Alberto Ibort and María Jiménez-Vázquez have contributed equally to the article.
© The Author(s) 2024
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