Charged Fluid Dynamics in Scalar-Tensor Theories of Gravity with Torsion

n scalar-tensor theories of gravity with torsion, the gravitational field is described in terms of a symmetric metric tensor $g$, a metric-compatible connection $\nabla$ with torsion, and a scalar field $\phi$. The main aim is to explore an interaction of a charged perfect fluid and a scalar field $\phi$ in a background electromagnetic and gravitational field described by \{$g$, $\nabla$, $\phi$\}. The interaction is based on an action functional $S_C$ of a charged perfect fluid that is invariant under global conformal rescalings. Using a variational principle, we obtain equations of motion for the charged perfect fluid. Moreover, we verify that these equations of motion are equivalent to the gauge identities obtained from the invariance of an action functional under spacetime dffeomorphisms and a local U(1) gauge group.