I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant.

  • Does dimensional regularization see "all" kinds of divergences?

    I mean - what does it exactly mean when one says that power law divergences and IR divergences disappear in the dimensional regularization. So is more regularization needed in general over and above dimensional regularization?

  • Does anything about the divergences get specially constrained if the theory is scale invariant?

    I have often heard it being said that dimensional regularization "preserves" scale invariance.

  • $\begingroup$ so does 'zeta regularization ' :D is an alternative to regularize finit integrals · $\int_{a}^{\infty}x^{m-s} $ for some finite 'a' $\endgroup$ – Jose Javier Garcia Apr 14 '13 at 12:39
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    $\begingroup$ @JoseJavierGarcia Can you kindly expand on your comment? What exactly did you mean? $\endgroup$ – user6818 Apr 16 '13 at 1:32
  • $\begingroup$ i meant that we can also use zeta regularization in renormalization :) , the main drawback of dimensional regularization is that it does not work for dimension-dependent quantities $\endgroup$ – Jose Javier Garcia Apr 16 '13 at 9:47
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    $\begingroup$ @Jose Javier Garcia In what precise sense do you mean "does not work"? Can you give some reference which shows how zeta-regularization helps with the RG flow of non-marginal operators? $\endgroup$ – user6818 Apr 24 '13 at 0:05
  • $\begingroup$ for zeta regualrization the best book is Elizalde's " ZETA REGULARIZATION TECHNIQUES" , or you have my paper for free :) vixra.org/pdf/1009.0047v4.pdf $\endgroup$ – Jose Javier Garcia Apr 24 '13 at 9:25

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