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Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization.
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See for instance, the famous (infamous?) comment by Paul Dirac: “I must say that I am very dissatisfied with the situation because this so-called ‘good theory’ does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small — not neglecting it just because it is infinitely great and you do not want it!”
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R. Kallosh, N=8 Supergravity on the Light Cone , arXiv:0903.4630 [hep-th]
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J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, A. S. Sakharov and E. K. G. Sarkisyan, Robust Limits on Lorentz Violation from Gamma-Ray Bursts Astropart. Phys. 25
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P. Hořava, Quantum Gravity at a Lifshitz Point , Phys. Rev. D 79
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