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As you may know in the context of dimensional regularization, integration is performed in d-dimension where d can take non-integer values. For example:

[itex]\int d^{d}q f(q^2)[/itex]=S[itex]_{D}[/itex][itex]\int_{0}^{∞}q^{q-1}f(q^2)dq[/itex]

My questions are:

1) Is the integration in d-dimension performed is well defined in the mathematical sense when integration is done for: 1<|q|<∞ rather than 0<q<∞:

[itex]\int_{|q|>1} d^{d}q f(q^2)[/itex]=S[itex]_{D}[/itex][itex]\int_{1}^{∞}q^{q-1}f(q^2)dq[/itex]

2)Are tadpole mass-less integrals still equal to zero in DR?

[itex]\int_{|q|>1} d^{d}q (q^2)^{β}[/itex]= 0 for β=1,2,...

Thanks in advance.

Best regards.

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# Integration in d-dimension

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