Tests of Lorentz invariance using hydrogen molecules

We discuss the consequences of Lorentz violation (as expressed within the Lorentz-violating extension of the standard model) for the hydrogen molecule, which represents a generic model of a molecular binding. Lorentz-violating shifts of electronic, vibrational and rotational energy levels, and of the internuclear distance are calculated. This offers the possibility of obtaining improved bounds on Lorentz invariance by experiments using molecules.