Quantum Field Theory by Mandl Franz Shaw Graham & Graham Shaw

Author:Mandl, Franz, Shaw, Graham & Graham Shaw [Mandl, Franz, Shaw, Graham & Shaw, Graham]
Language: eng
Format: epub
Publisher: Wiley
Published: 2013-06-03T14:00:00+00:00

where, for example, r3 means that the third quark is in an r state etc. The coefficients αi(i = 1, 2, …, 6) are constants whose values are restricted by the remaining confinement conditions (11.15). For example, imposing and using Eqs. (11.13) and (11.14) gives

Similar results follow from the other conditions (11.15). Together they uniquely determine the wavefunction to be

(11.17)

up to an arbitrary normalization, where a sum over repeated indices i = 1, 2, 3 etc. is understood as usual. The antisymmetric alternating symbol εijk is equal to +1 (−1) for (i, j, k) an even (odd) permutation of (1, 2, 3) and vanishes if two or more indices are the same. Because it is totally antisymmetric, applying the Pauli principle to the full wavefunction leads directly to the result that the combined space/spin wave-function ψ must be symmetric under the interchange of identical quarks, as assumed in the quark model.

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