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There are some confusions regarding infrared (IR) divergences in gauge theory:

  • What is the primary reason for the appearance of IR divergences in gauge theory? Anything other than the existence of massless particles in the spectrum of the theory.

  • Why there is no IR divergence for massive theories? The propagator is given by: $$K(p)\propto\frac{1}{p^2-m^2}$$ Therefore, it is expected that the internal momentum integration crosses the pole given by mass. If $i\varepsilon$-prescription is used to avoid this, why does it can not be used in the case of massless theories with propagator proportional to $\frac{1}{p^2}$?

  • Do IR divergences appear only at the loop-level?

  • The S-matrix of a QFT is defined by assuming that the interactions die off at spatial infinity. But in a theory with massless particles, this can not be assumed. Then how should we interpret the results of scattering amplitude computations in gauge theory?

  1. What is the primary reason for the appearance of IR divergences in gauge theory? Anything other than the existence of massless particles in the spectrum of the theory.

  2. Why there is no IR divergence for massive theories? The propagator is given by: $$K(p)\propto\frac{1}{p^2-m^2}$$ Therefore, it is expected that the internal momentum integration crosses the pole given by mass. If $i\varepsilon$-prescription is used to avoid this, why does it can not be used in the case of massless theories with propagator proportional to $\frac{1}{p^2}$?

  3. Do IR divergences appear only at the loop-level?

  4. The S-matrix of a QFT is defined by assuming that the interactions die off at spatial infinity. But in a theory with massless particles, this can not be assumed. Then how should we interpret the results of scattering amplitude computations in gauge theory?

There are some confusions regarding infrared (IR) divergences in gauge theory:

  • What is the primary reason for the appearance of IR divergences in gauge theory? Anything other than the existence of massless particles in the spectrum of the theory.

  • Why there is no IR divergence for massive theories? The propagator is given by: $$K(p)\propto\frac{1}{p^2-m^2}$$ Therefore, it is expected that the internal momentum integration crosses the pole given by mass. If $i\varepsilon$-prescription is used to avoid this, why does it can not be used in the case of massless theories with propagator proportional to $\frac{1}{p^2}$?

  • Do IR divergences appear only at the loop-level?

  • The S-matrix of a QFT is defined by assuming that the interactions die off at spatial infinity. But in a theory with massless particles, this can not be assumed. Then how should we interpret the results of scattering amplitude computations in gauge theory?

There are some confusions regarding infrared (IR) divergences in gauge theory:

  1. What is the primary reason for the appearance of IR divergences in gauge theory? Anything other than the existence of massless particles in the spectrum of the theory.

  2. Why there is no IR divergence for massive theories? The propagator is given by: $$K(p)\propto\frac{1}{p^2-m^2}$$ Therefore, it is expected that the internal momentum integration crosses the pole given by mass. If $i\varepsilon$-prescription is used to avoid this, why does it can not be used in the case of massless theories with propagator proportional to $\frac{1}{p^2}$?

  3. Do IR divergences appear only at the loop-level?

  4. The S-matrix of a QFT is defined by assuming that the interactions die off at spatial infinity. But in a theory with massless particles, this can not be assumed. Then how should we interpret the results of scattering amplitude computations in gauge theory?

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Infrared Divergences in Gauge Theories

There are some confusions regarding infrared (IR) divergences in gauge theory:

  • What is the primary reason for the appearance of IR divergences in gauge theory? Anything other than the existence of massless particles in the spectrum of the theory.

  • Why there is no IR divergence for massive theories? The propagator is given by: $$K(p)\propto\frac{1}{p^2-m^2}$$ Therefore, it is expected that the internal momentum integration crosses the pole given by mass. If $i\varepsilon$-prescription is used to avoid this, why does it can not be used in the case of massless theories with propagator proportional to $\frac{1}{p^2}$?

  • Do IR divergences appear only at the loop-level?

  • The S-matrix of a QFT is defined by assuming that the interactions die off at spatial infinity. But in a theory with massless particles, this can not be assumed. Then how should we interpret the results of scattering amplitude computations in gauge theory?