Alladi Ramakrishnan Hall

A Gauge invariant formulation of QCD via canonical transformations

Sreeraj T. P.

IMSc

Analytical understanding of low energy properties of QCD has been an important outstanding problem in modern physics for a long time. The situation with standard formulation of QCD is as follows. QCD is formulated as a theory of quarks and gluon fields which are gauge variant. But, only gauge invariant states are observable in nature. The situation is then remedied by imposing gauge invariance condition as a constraint. This is often a non-trivial exercise (Gauss law constraint, Faddeev Popov Gauge fixing etc). One is then tempted to ask whether it is possible to formulate gauge theories (QCD) in terms of gauge invariant fields and thereby make it completely transparent. In this talk, I will discuss a method to construct a gauge invariant formulation of SU(N) gauge theory with (fermionic) matter fields on the lattice. Starting with the standard formulation based on quarks and gluons and gauge invariance constraints, we will construct an exact canonical transformation to a set of gauge invariant variables. This will be first illustrated in a Z2 gauge theory with matter fields and then generalised to an SU(N) gauge theory.