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We consider the $g$ factor of a spin-1/2 particle (electron or muon) bound byan arbitrary central field. We present an approach which allows one to expressthe relativistic $g$ factor in terms of the binding energy. We derive thegeneral expression for the correction to the $g$ factor caused by a deviationof the central potential from the Coulomb one. As the application of thismethod, we consider the corrections to the $g$ factor due to the finite nuclearsize, including vacuum polarization radiative correction. The effect of theanomalous magnetic moment is also taken into account.Comment: 4 pages, RevTeX, some comments adde

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>factor of an electron or muon bound by an arbitrary central potential

gfactor of an electron or muon bound by an arbitrary central potential