New Perspectives on Einstein’s E = MC2 by Young Suh Kim and Marilyn E Noz

Author:Young Suh Kim and Marilyn E Noz
Language: eng
Format: epub
Publisher: World Scientific Publishing Co. Pte. Ltd.
Published: 2019-08-15T00:00:00+00:00

However, they are boosted by

which are applicable to the undotted and dotted spinors, respectively. These two matrices commute with each other, and also with the rotation matrix Z(ϕ) of Eq. (7.45). Since K3 and J3 commute with each other, we can work with the matrix Q(η, ϕ) defined as

When this combined matrix is applied to the spinors,

If the particle is at rest, we can explicitly construct the combinations

to obtain the spin-1 state, and

for the spin-0 state. This results in four bilinear states. In the SL(2, c) regime, there are two dotted spinors which result in four more bilinear states. If we include both dotted and undotted spinors, there are 16 independent bilinear combinations. They are given in Table 7.2. This table also gives the effect of the operation of Q(η, ϕ).

Among the bilinear combinations given in Table 7.2, the following two equations are invariant under rotations and also under boosts:

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