Dimensional regularization and IR divergences and scale invariance

Question

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.

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user user6818

Comments

so does 'zeta regularization ' :D is an alternative to regularize finit integrals · $\int_{a}^{\infty}x^{m-s} $ for some finite 'a'

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user Jose Javier Garcia

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@JoseJavierGarcia Can you kindly expand on your comment? What exactly did you mean?

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user user6818

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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

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user Jose Javier Garcia

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@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?

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user user6818

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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

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user Jose Javier Garcia

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@JoseJavierGarcia Kindly put up your paper on arxiv so that it becomes legitimate to read/cite it!

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user user6818

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i have no academic affiliation so they do not let me put papers in arxiv.org anyway you can check the equations :) to see they are corrects

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user Jose Javier Garcia

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García, José Javier prespacetime.com/index.php/pst/article/view/498 The Application of Zeta Regularization Method to the Calculation of Certain Divergent Series and Integrals Refined Higgs, CMB from Planck, Departures in Logic, and GR Issues & Solutions vol 4 Nº 3 prespacetime journal prespacetime.com/index.php/pst/issue/view/41/showToc

This post imported from StackExchange Physics at 2014-08-07 15:39 (UCT), posted by SE-user Jose Javier Garcia