Magnetofluid Unification in the Yang - Mills

The Yang-Mills magnetofluid unification is constructed using lagrangian approach by imposing certain gauge symmetry to the matter inside the fluid. The model provides a general description for relativistic fluid interacting with Abelian or non-Abelian gauge field. The differences with the hybrid magnetofluid model are discussed, and few physical consequences of this formalism are worked out. PACS : 12.38.Mh, 11.15.-q, 47.75.+f Some experimental discoveries and studies suggest that the deconfined quark gluon matter is behaving more like a quark gluon plasma (QGP) liquid [1, 2, 3]. This fact motivates tremendous works in constructing the non-Abelian fluid models like magnetohydrodynamics [4, 5, 6, 7, 8, 9, 10, 11, 12]. In some recent models [9, 10, 11], the relativistic hot fluid was described in terms of hybrid magnetofluid field which unifies the electromagnetic and fluid fields. The unification is represented by the effective field strength tensor, Mμν ≡ Fμν +m/qSμν combining appropriately weighted electromagnetic and fluid fields. The model has Email : [email protected], [email protected] Email : [email protected] Email : [email protected], [email protected] further been generalized to the non-Abelian case [10]. Also its topological structures has been investigated in detail to model the glueballs [11]. In this Letter, we follow the same line but with different starting point using lagrangian approach and imposing certain gauge symmetry on it. This approach is intended to improve the Yang-Mills magnetofluid unification model [10] in two aspects : • From field theory point of view, the fluid and another gauge fields should physically be different fields, and then should have independent kinetic terms in the lagrangian. Deploying the above effective field tensor would lead to the unphysical two point interaction connecting two different fields from the gauge invariance kinetic term MμνM μν in the lagrangian. • The hybrid strength tensor Mμν suggests that the fluid and another Abelian or non-Abelian gauge fields are gauge invariance under a single gauge transformation and both should belong to the same Lie group. This requirement is actually necessary since the formalism relies on the Lorentz force equation. This also avoids us to deal with, for instance, the case of non-Abelian fluid interacting with an (Abelian) electromagnetic field. In order to overcome such problems, we propose local and independent gauge symmetries for each field of fluid and another gauge boson interacting with it, inspired by the unified theory known in particle physics. The model is able to deal with some scenarios like : (i) non-Abelian fluid interacting with non-Abelian gauge field under G(n)F ⊗ G(n)G symmetry; (ii) non-Abelian fluid interacting with an (Abelian) electromagnetic field under G(n)F ⊗ U(1)G symmetry; and (iii) Abelian fluid interacting with an electromagnetic field under U(1)F ⊗ U(1)G symmetry, i.e. the original magnetofluid model. Here F and G denote the fluid and another gauge fields respectively. Note that G(n) could be any n dimensional Lie group like SU(n). Following the basic procedure in lagrangian approach, we start from the following matter lagrangians,