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According to Noether's theorem, Every continuous symmetry of the action leads to a conservation law. For example, conservation of linear momentum corresponds to translational symmetry, conservation of angular momentum corresponds to rotational symmetry.

My question is on the conservation of baryon number, lepton number and strangeness. What type of symmetry does imply when the above mentioned quantities are conserved in a system?

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Conservation of baryon number <-> Global gauge invariance

Conservation of lepton number <-> U(1) symmetry

Conservation of strangeness is only for the strong (SU(3) symmetry) and electromagnetic interactions ( local U(1) gauge invariance)

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    $\begingroup$ Please don't call it "global gauge invariance", it's a phase rotation of the baryon wavefunctions, which is not really a "gauge transformation", it's a global field transformation. You are not describing the symmetry, you are only giving it a suboptimal name. $\endgroup$ – Ron Maimon Oct 1 '12 at 7:07

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