General Principles of Brane Kinematics and Dynamics

We consider branes as "points" in an infinite dimensional brane space ${\cal M}$ with a prescribed metric. Branes move along the geodesics of ${\cal M}$. For a particular choice of metric the equations of motion are equivalent to the well known equations of the Dirac-Nambu-Goto branes (including strings). Such theory describes "free fall" in ${\cal M}$-space. In the next step the metric of ${\cal M}$-space is given the dynamical role and a corresponding kinetic term is added to the action. So we obtain a background independent brane theory: a space in which branes live is ${\cal M}$-space and it is not given in advance, but comes out as a solution to the equations of motion. The embedding space ("target space") is not separately postulated. It is identified with the brane configuration.