Gaussian ensemble of 2x2 pseudo-Hermitian random matrices

We present a random matrix theory for systems invariant under the joint action of parity, P, and time reversal, T, and, more generally, for pseudo-Hermitian systems. This brings out the appearance of the metric in a systematic way so that consistency with the postulates of quantum mechanics is maintained. Here we specialize only to 2 x 2 matrices and we construct a pseudo-unitary group. With explicit examples, nearest-neighbour level-spacing distributions for various classes of ensembles are found to exhibit a degree of level repulsion different from those hitherto known. This work is not only relevant to quantum chaos, but also to two-dimensional statistical mechanics and consistent nonlocal relativistic theories.