Hamiltonian approach to Lattice QCD: Nonequilibrium and Finite density

I present an approach to lattice QCD using the Hamiltonian formalism for non-equilibrium and finite density. This approach can circumvent the sign problem of QCD that arises from importance sampling. Because the gauge theory has infinite dimensional Hilbert space even on a finite lattice, due to the gauge field being a boson, and because of the large redundancy in degrees of freedom associated with gauge symmetry, it is necessary to introduce regularization to perform calculations. To this end, we employ a q-deformed gauge theory as a regularization technique that preserves the properties of the original gauge theory. As applications of Hamiltonian formalism, I show our results on the thermalization process on a small lattice system, and the thermodynamics behavior at finite density in (1+1)-dimensional system using the density matrix renormalization group technique.