ИСТИНА

According to Noether’s theorem, each continuous symmetry of a physical system corresponds to a certain conservation law. Continuous symmetry is the invariance with respect to a family of continuous transformations. We will start with a proof of Noether’s theorem in a book published by Kleinert. In this book, all formulas related to fields do not specify the domains in infinite-dimensional spaces, so they need to be improved. Since invariances and conservation laws in ordinary Euclidean spaces have been systematically studied, we study the translational invariance of generalized measures in Hilbert space from a new paper.