Quantum Fluctuations in Noether's Theorem

arXiv:2611.08906v1 Announce Type: new Abstract: When deriving the expression for the Noether's current one obtains a term that is an integral over the Euler-Lagrange equation. This term vanishes along the classical path and so does not contribute to the current. However, quantum particles do not necessarily follow the classical path; this concept is the basis of Feynman's path integral quantization formalism. Thus, for a quantum system, the Euler-Lagrange term does not vanish and, hence, corresponds to a quantum fluctuation of the Noether's current owing to the system deviating from the classical path. Here, we compute this quantum fluctuation from Noether's theorem and the path integral formalism.