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arivero

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The Higgs mechanism allows to give masses to massless particles. In extra dimensions there is another mechanism

Any hint about earlier uses of this idea?

Nuc Phys B said:to understand the basic idea (see also a discussion by Palla), suppose that in a 4+n dimensional theory we have a massless spin one half fermion. It satisfies the 4+n dimensional Dirac equation

[tex]\kern+0.25em /\kern-0.80em D \psi =0 [/tex]

or explicitly

[tex]\sum_{i=1}^{4+n} \gamma^i D_i \psi=0[/tex]

This Dirac operator can be written in the form

[tex]\kern+0.25em /\kern-0.80em D^{(4)} \psi +\kern+0.25em /\kern-0.80em D^{(int)}\psi =0 [/tex]

where

[tex]\kern+0.25em /\kern-0.80em D^{(4)} \equiv \sum_{i=1}^{4} \gamma^i D_i[/tex] is the ordinary four-dimensional Dirac operator, and [tex]\kern+0.25em /\kern-0.80em D^{(int)}\equiv \sum_{i=5}^{4+n} \gamma^i D_i[/tex] is the Dirac operator in the internal space of n compact dimensions.

The expression (above) immediately shows that the eigenvalue of [tex]\kern+0.25em /\kern-0.80em D^{(int)}[/tex] will be observed in practice as the four-dimensional mass.

Any hint about earlier uses of this idea?

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