Search for variation of the fundamental constants in atomic, molecular, and nuclear spectra

The search for variation of the fundamental constants such as the fine-structure constant alpha (alpha = e(2)/hc) and the ratios of fundamental masses (for example, electron-to-proton mass ratio mu = m(e)/m(p)) is reviewed. Strong emphasis is given to establishing the relationships between the change in the measured frequencies of atomic, molecular, or nuclear transitions and the corresponding change of the fundamental constants. Transitions in which the sensitivity of the frequency change to the variation of the fine-structure constant is strongly enhanced are discussed and most recent experimental results are presented. Most attention is given to the use of atomic, molecular, and nuclear transitions in the study of quasar absorption spectra and in atomic clock experiments.