Abstract
The chapter discusses some important symmetries in the field theory that lead to the QCD Lagrangian. A method of reliably calculating thermodynamic quantities in the nonperturbative regime of QCD, necessary to determine the order of the phase transition and critical temperature, is needed. The Lagrange equation for the fermion field is the Dirac equation for the adjoint field. In the field theory, Noether's theorem states that for a system described by a Lagrangian, any continuous symmetry transformation that leaves the action invariant implies a conserved current. Lattice gauge theory reformulates QCD on a lattice of discrete space-time points. The spacing among lattice points provides a finite distance scale. This lattice spacing gives a minimum distance and thus also a maximum momentum scale that acts as a momentum cut-off in the integrations. The interaction term employs finite difference techniques to discretize the derivative in terms of the link variables required to connect the fermion field to its conjugate.
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