A Lagrangian path integral approach to the qubit
arxiv(2024)
摘要
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.
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