Fundamental physical equations uniquely determined by their symmetry groups

Abstract

In all the above theorems both demands (that L is analytic and that L is scale invariant) are essential, i.e., if we consider these theorems as determining a new axiomatics for physical theories, then all these new axiomes are independent.

For example, in theorem I, if one do not demand invariance, then L=R + aR² is possible, if we avoid demand that L is analytic — then L = =√R_ijR^ij is possible.

The authors express their sincere acknoledgements to those who took part in the discussion of different parts of this paper: academician A.D.Alexandrov, A.I.Cudnovsky, A.I.Fet, V.N.Folomeshkin, A.A.Grib, A. K.Guts, V.K.Ionin, O.M.Kosheleva, Yu.I.Kulakov, I.A.Kunin, G.B.Rumer and P.G.Vroegindewey.