IR divergences by analytic continuation of parameters

In summary, the discussion involved proposing a method to avoid IR divergence by setting the regularized value as F(-a), where F is the integral. It was suggested that this method is valid for analytic continua with respect to certain parameters in the real or complex plane.
  • #1
zetafunction
391
0
i had a discussion with a physicist i proposed that in order to avoid the IR divergence

[tex] \int_{0}^{\infty}dx(x-a)^{-3}x^{2} [/tex]

we could propose as regularized value the value of F(-a) , where F is the integral

[tex] \int_{0}^{\infty}dx(x+b)^{-3}x^{2} [/tex] so if we could regularize this simply setting b=-a the IR divergence dissapear

is this method valid , to analytic continua with respect to some parameters into the real or complex plane.
 
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  • #2
zetafunction said:
i had a discussion with a physicist i proposed that in order to avoid the IR divergence

[tex] \int_{0}^{\infty}dx(x-a)^{-3}x^{2} [/tex]

we could propose as regularized value the value of F(-a) , where F is the integral

[tex] \int_{0}^{\infty}dx(x+b)^{-3}x^{2} [/tex] so if we could regularize this simply setting b=-a the IR divergence dissapear

is this method valid , to analytic continua with respect to some parameters into the real or complex plane.

it is valid whenever you know (or can safely assume) that the quantity you want to compute is analytic along a path from a to -b.
 

Related to IR divergences by analytic continuation of parameters

1. What are IR divergences by analytic continuation of parameters?

IR divergences by analytic continuation of parameters refer to a mathematical method used in theoretical physics to handle divergences that arise in the calculation of scattering amplitudes. This method involves analytically continuing the parameters of the problem to a complex plane, where the divergences can be regulated and the results can be obtained in a more rigorous manner.

2. Why do IR divergences occur in theoretical physics?

IR divergences occur in theoretical physics because of the nature of quantum field theories. These theories involve the interaction of particles at different energy scales, and when these scales become infinite, the calculations become non-perturbative and lead to divergent results. IR divergences are a common problem in many quantum field theories, including quantum chromodynamics (QCD) and electroweak theory.

3. How are IR divergences by analytic continuation of parameters regulated?

IR divergences by analytic continuation of parameters are typically regulated using a process called dimensional regularization. This method involves performing calculations in a higher number of dimensions and then analytically continuing the results to the desired number of dimensions. This approach allows for the divergences to be regulated in a systematic and consistent manner.

4. Can IR divergences be physically observed?

No, IR divergences cannot be physically observed. They are mathematical artifacts that arise in certain calculations in theoretical physics. However, their presence can have physical consequences, as they can affect the accuracy of predictions and the interpretation of experimental results.

5. How are IR divergences by analytic continuation of parameters related to renormalization?

IR divergences by analytic continuation of parameters are closely related to renormalization. Renormalization is a process used to remove infinities from calculations in quantum field theories, and IR divergences are one type of infinity that must be regulated. By using analytic continuation of parameters, renormalization can be carried out in a more rigorous and systematic way, leading to more accurate predictions in theoretical physics.

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