San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

Quantum Field Theory
and Lorentz Invariance

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 = KQ/r for r > R
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

σ = Q/[(4/3)π(R³ − (R-D)³)]

Here is an example.

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