Effective theory of theT- andP-breaking superconducting state

We propose an effective theory of superconductivity based on a microscopic theory of the T- and P-breaking spin-liquid state. There are two independent gauge invariances broken by two separate condensates. The theory may be useful for phenomenological calculations. In particular, we find that ${\mathrm{H}}_{\mathrm{c}1}$ are different for magnetic fields with opposite orientations. We also find that the polarization of an electromagnetic wave is rotated after reflection from these T- and P-breaking superconductors.