Left-handed coordinate

Consider for example the theory under discussion, namely, quantum electrodynamics under the circumstance that the frame of reference with respect to which phenomena are described is changed from a right-handed to a left-handed coordinate system, i.e., from one in which the space-time coordinates are labeled by to one in which they are labeled by sc, with... 

Particle-Antipartide Conjugation.—If quantum electrodynamics is invariant under space inversion, then it does not matter whether we employ a right- or left-handed coordinate system in the description of ptnely electrodynamio phenomena. To speak of right and left is, an arbitrary convention in a worlcl ip which only electrodynamics operates. 

Overlap of d orbitals leading to the formation of a quadruple bond between two metal atoms. Note that the z axis of each metal atom is taken to point toward the other, such that if a right-handed coordinate system is used for the atom on the left, a left-handed coordinate system must be used for the atom on the right. 

A cover is a horizontal string of at least p such objects, where the distance between two neighboring objects must be less than q points (p and q are parameters typical of a metaphase cell). The starting coordinates of a cover (xs, ys) is the left-hand coordinates of its left most object, and the ending coordinate of this cover (Xe, ye) is the right-hand coordinates of its right most object, and... 

There is not generally accepted rule for the choice of the coordirrate system for right-handed and left-handed quartz crystals. Coordinate jc-axis is chosen generally in the direction of electrical a-axis and z-axis is in the direction of the optical c-axis. Cady and several other authors use right-handed coordinate system for right-handed quartz and left-handed coordinate system for left-handed quartz. On the contrary. 

Figure 3.2 depicts the three-dimensional version of Cartesian coordinates. We define the x and y axes as before, and erect the z axis through the origin and perpendicular to the X and y axes. We will use a right-handed coordinate system like that of Figure 3.1. For this case, if the thumb of the right hand points in the direction of the positive x axis and the index finger points in the direction of the positive y axis, the middle finger can point in the direction of the positive z axis. If the left hand must be used for such an alignment, the coordinate system is called a left-handed coordinate system.

The Euler equations are invariant with respect to changes of reference frame that leave the symmetry unchanged, for example, an inversion of the z axis to form a left-handed coordinate system. 

---