Shay you want here is Matthew D. Schwarz, Quantum Theory and the Standard Model, chapter 15.
(or the original paper by CasiMir cited in the above book chapter.
Zeta regularisation is a much saner way to explain it.
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in a physics context .. suppose that the laws of physics you have are only valid up to some energy scale E, where E is presumed large.
The physical quantity you ’re interested in is f(E) - g(E).
lim E → infinity of f(E) and g(E) is infinite, so can’t safely exchange the order of the limits and the subtraction. But lim E → infinity (f(E) - g(E)) exists and is finite, so you’re good to go, and the result is insensitive to what the energy scale E actually is,
Shay you want here is Matthew D. Schwarz, Quantum Theory and the Standard Model, chapter 15.
(or the original paper by CasiMir cited in the above book chapter.
Zeta regularisation is a much saner way to explain it.
====
in a physics context .. suppose that the laws of physics you have are only valid up to some energy scale E, where E is presumed large.
The physical quantity you ’re interested in is f(E) - g(E).
lim E → infinity of f(E) and g(E) is infinite, so can’t safely exchange the order of the limits and the subtraction. But lim E → infinity (f(E) - g(E)) exists and is finite, so you’re good to go, and the result is insensitive to what the energy scale E actually is,