Exact laws




A partial listing of physical conservation equations due to symmetry that are said to be exact laws, or more precisely have never been proven to be violated:

Conservation Law Respective Noether symmetry invariance Number of dimensions
Conservation of mass-energy Time-translation invariance Lorentz invariance symmetry 1 translation along time axis
Conservation of linear momentum Space-translation invariance 3 translation along x,y,z directions
Conservation of angular momentum Rotation invariance 3 rotation about x,y,z axes
Conservation of CM (center-of-momentum) velocity Lorentz-boost invariance 3 Lorentz-boost along x,y,z directions
Conservation of electric charge Gauge invariance 1⊗4 scalar field (1D) in 4D spacetime (x,y,z + time evolution)
Conservation of color charge SU(3) Gauge invariance 3 r,g,b
Conservation of weak isospin SU(2)L Gauge invariance 1 weak charge
Conservation of probability Probability invariance 1 ⊗ 4 total probability always = 1 in whole x,y,z space, during time evolution

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