In general someone works with [itex]d[/itex] dimensions, and at some point makes an expansion around [itex]d=4[/itex], by writing [itex]d \rightarrow 4 [/itex],(adsbygoogle = window.adsbygoogle || []).push({});

This [itex]d \rightarrow 4 [/itex] (or [itex] \epsilon = \frac{4-d}{2} \rightarrow 0[/itex] in most textbooks) is really confusing me in the dimensional regularization... I don't understand how you can "approach" the dimensions to 4, since they can either be 4 or 5 or 3 or some other natural number... eg 4.1 or 4.001 dimensions doesn't make sense, and so do powers of [itex]\epsilon[/itex]. [itex]\epsilon[/itex] can be either 0 or at next best jump, [itex]1/2[/itex]. However I haven't found any textbook that goes through that in a comprehensive way (if there is any).

Is it just a mathematical abuse?

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# Dimensional Regularizaiton (dimensions d)

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