Maximal Abelian gauge has been a particular choice to study dynamical generation of offdiagonal gluon masses in QCD. This gauge is a special case of Abelian projection. Massive offdiagonal gluons are considered a clue to Abelian dominance. Here we propose a gauge condition which is quadratic in fields and which does not fall in the class of Abelian projection. However it does generate off-diagonal gluon masses dynamically thus hinting at Abelian dominance in this gauge too.

We study the partial decay widths of the charmonium states (J/ψ, ψ(3686), ψ(3770), χ c0 , χ c2 ) to DD (D + D − or D 0D0 ) in isospin asymmetric nuclear matter, in the presence of strong magnetic fields.The in-medium partial decay widths of charmonium states to DD are calculated within a light quarkantiquark pair creation model, namely the 3 P 0 model, using the in-medium masses of the charmonia as well as D andD mesons in the magnetized nuclear matter, obtained within a chiral effective model.The presence of a magnetic field leads to Landau quantization of the energy levels of the proton in the nuclear medium. The effects of magnetic field and isospin asymmetry on the charmonium decay widths to DD are found to be quite prominent. The effects of the anomalous magnetic moments have also been taken into consideration for obtaining the in-medium masses of these heavy flavour mesons, used to calculate the partial decay widths of the charmonium states. The medium modifications of the charmonium decay widths can have observable consequences on the production of the charmed mesons in high energy asymmetric heavy ion collision experiments.

The Gribov ambiguity exists in various gauges except algebraic gauges. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S 3 , when a proper boundary condition on the gauge configuration is taken into account. Thus, providing one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.

We consider SU (N ) QCD in a new quadratic gauge which highlights certain characteristic of the theory in the non-perturbative sector. By considering natural hermiticity property of the ghost fields we cast this model as non-Hermtian but symmetric under combined Parity (P) andTime reversal (T) transformations. We explicitly study the PT phase transition in this model. This is very first such study in the non-Hermitian gauge theory. The ghost fields condensate as a direct consequence of spontaneous breaking of PT symmetry. This leads to realize the transition from deconfined phase to confined phase as a PT phase transition in this system. The hidden Csymmetry in this system is identified as inner automorphism in this theory. Explicit representation is constructed for the C-symmetry.