TY - JOUR
T1 - Dynamics and scattering of a massless particle
AU - Soffer, Avy
N1 - Funding Information:
I wish to thank I.M. Sigal for useful discussions. Part of this work was done while the author visited the IHES, France. A. Soffer was partially supported by NSF grant number DMS-0903651 and DMS-1201394 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - We estimate the probability of a photon to move faster than light, under the Einstein dynamics which, unlike the wave equation or Maxwell wave dynamics, has singular dispersion relation at zero momentum. We show that this probability goes to zero with time, using propagation estimates suitably multi-scaled to control the contribution of low frequencies. We then prove minimal velocity bounds.
AB - We estimate the probability of a photon to move faster than light, under the Einstein dynamics which, unlike the wave equation or Maxwell wave dynamics, has singular dispersion relation at zero momentum. We show that this probability goes to zero with time, using propagation estimates suitably multi-scaled to control the contribution of low frequencies. We then prove minimal velocity bounds.
KW - Photon dynamics
KW - Propagation estimates
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U2 - 10.1016/j.jfa.2016.06.003
DO - 10.1016/j.jfa.2016.06.003
M3 - Article
AN - SCOPUS:84991712996
SN - 0022-1236
VL - 271
SP - 1043
EP - 1086
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 5
ER -