Notations for the Density Matrix and Its Subsets

In Section 11.2 we note that p is usually expressed in a rotating frame. Unless there is a specific application in which it is important to distinguish between the laboratory and rotating frames, we continue to use p as the symbol, regardless of coordinate system. 

In Section 11.3 we find that the density matrix for a spin system at equilibrium can be separated into the unit matrix 1 and other terms pertaining to populations of spin states. The unit matrix is unaffected by rf pulses or any other evolution of the density matrix hence it is conventional to delete it, and we do so. Some authors introduce a new symbol for the truncated matrix, but most do not. We continue to use the symbol p for this truncated density matrix. 

We know that rf pulses rotate magnetization vectors and alter the state of the spin system. To examine such effects quantitatively in terms of alterations in the density matrix, it will be helpful to express the density matrix in the rotating frame of reference. 

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