Notational Conventions and Choice of Units

Several conventions are used throughout this book. We may summarize some basic principles of notation here. 

Cartesian vectors with three components, so-called 3-vectors, are indicated by boldface type, e.g., the position vector r. Relativistic four-component vectors, so-called 4-vectors, are denoted by normal type. If not otherwise stated, all vectors irrespective of their dimension are assumed to be column vectors. The corresponding row vector is given by the transposed quantity, e.g., 

A dot on top of a symbol for a physical quantity denotes the total time derivative of that quantity, e.g., r = dr/dt. Partial time derivatives are symbolized by d/dt. The spatial derivatives in one- or three-dimensional space are symbolized by A x) or and V A(r), respectively. 

The same symbols will be used for classical quantities and also for the corresponding operators of the quantized formulation. Consequently, p might s)mibolize classical momentum as well as the quantum mechanical momentum operator p = —ihV for example. The detailed meaning of symbols will become obvious from the context. Occasionally one might encounter a hat on top of a s)mibol chosen in order to emphasize that this symbol denotes an operator. However, a hat on top of a vector may also denote the corresponding unit vector pointing in the direction of the vector, e.g., the position vector may therefore be expressed asr = rr. 

Most quantities require extensive use of indices. In principle, we may distinguish the following sets of indices  

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