TABLE OF CONTENTS Any set of transformations either involving space-time or some internal space can be best understood when described in terms of a change in reference frame. Continuous as well as discrete transformations can be discussed within this kind of framework. The previous chapter dealt with continuous symmetries, and we now turn to discrete transformations.
As mentioned in previous chapters, parity, otherwise known as space inversion, is a transformation that takes us from a right handed coordinate frame to a left handed one, or vice versa. Under this transformation, which we denote by the symbol P, the space-time four-vector changes as follows:
| (11.1) |  |
It is important to recognize that the parity operation is distinct from spatial rotations because a left handed coordinate system cannot be obtained from a right handed one through any combination of rotations. In fact, rotations define a set of continuous transformations, whereas the inversion of space coordinates does not. It is clear therefore that the quantum numbers corresponding to rotations and parity are distinct.
Classically, the components of position and momentum vectors change sign under inversion of coordinates, while their magnitudes are preserved
| (11.2) |  |
This defines the behavior of normal scalar and vector quantities under space inversion. There are, however, scalar and vector quantities that do not transform under parity as shown in Eq. (11.2). Thus, for example, the orbital angular momentum, which changes like a vector under a rotation of coordinates, and which we therefore regard as a vector, behaves under space inversion...
