Beyond particles and localities in quantum matters

Many properties of strongly correlated materials behave differently from those obeying the standard theory of metals. Explaining such anomalous properties may require one to consider a non-traditional model. In this dissertation, we construct several phenomenological models based on the notions of unparticles and nonlocalities to explain some of the exotic properties of the high temperature cuprate superconductors. The properties of the cuprates that we investigate include the fractional power-law in optical conductivity, the power-law liquid form of the scattering life-time, the violation of the conductivity sum rule, and the appearance of the anomalous dimension for the current. Our results suggest that the correct description of the low-energy theory of the normal state of the cuprates could involve unparticles and nonlocal actions