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Fractional Soft Limits of Scattering Amplitudes
Tomáš Brauner1, Angelo Esposito2, Riccardo Penco3
1Department of Mathematics and Physics, University of Stavanger, N-4036 Stavanger, Norway.
The scattering amplitude of phonons, which are Nambu-Goldstone bosons in solids, can unexpectedly vanish with fractional powers of momentum. This challenges the conventional integer power scaling for soft boson scattering.
Area of Science:
- Condensed matter physics
- Quantum field theory
- Phononics
Background:
- Nambu-Goldstone bosons typically exhibit scattering amplitudes scaling with integer powers of their momentum.
- This expectation is based on theories with unbroken Lorentz invariance.
Purpose of the Study:
- To investigate the scattering amplitude of phonons (Nambu-Goldstone bosons) in 2→2 scattering processes in solids.
- To determine if the common lore of integer power scaling holds for soft phonons.
Main Methods:
- Analysis of 4-point scattering amplitudes for phonons in solids.
- Consideration of the role of broken Lorentz invariance and collinear kinematics.
Main Results:
- Demonstrated that phonon scattering amplitudes can vanish with fractional powers of the soft momentum.
- Identified the breaking of Lorentz invariance and collinear kinematics as key factors.
Conclusions:
- The common lore of integer power scaling for soft boson scattering is not universally applicable.
- Fractional power scaling can occur in nonrelativistic, shift-invariant theories due to specific kinematic conditions.
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