These are all defined in an analogous way to above, although the minus signs in the boost generators are conventional. Physically, the generators of the Lorentz group correspond to important symmetries in spacetime: are the "rotation generators" which correspond to angular momentum, and are the "boost generators" which correspond to the motion of the system in spacetime. The derivative of any smooth curve with in the group depending on some group parameter with respect to that group parameter, evaluated at , serves as a definition of a corresponding group generator , and this reflects an infinitesimal transformation away from the identity. The smooth curve can always be taken as an exponential as the exponential will always map smoothly back into the group via for all ; this curve will yield again when differentiated at .