San José State University |
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applet-magic.comThayer WatkinsSilicon Valley & Tornado Alley USA |
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Quantum Field Theory and Lorentz Invariance |
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Quantum Field Theory presumes a quantum field emanates from a charged point particle, but that singularity means there is an infinite self-energy
for the field. That infinite enerrgy leads to other infinities that must be resolved by the methods based upon the so-called *renormalization group*.

It alleged that the field with the point particle singularity is necessary for Quantum Field Theory its invariance to Lorentz transformations means QFT satisfies the Special Theory of Relativity. Supposedly a field emanating from a charged spherical shell or ball of radius R cannot have Lorentz invariance. The field for such charged particle would be of the following form

E = 0 for r < (R-D)

E = K[4/3πσ(r³−(R−D)³ for (R-D)≤r<R

where K is a parameter, D is the thickness of the shell. The spatial density of the charge σ in the last expression is given by

Here is an example.

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