Einstein, Wigner, and Feynman: From E = mc^{2} to Feynman's decoherence via Wigner's little groups

Abstract

The 20th-century physics starts with Einstein and ends with Feynman. Einstein introduced the Lorentz-covariant world with E = mc^{2}. Feynman observed that fast-moving hadrons consist of partons which act incoherently with external signals. If quarks and partons are the same entities observed in different Lorentz frames, the question then is why partons are incoherent while quarks are coherent. This is the most puzzling question Feynman left for us to solve. In this report, we discuss Wigner's role in settling this question. Einstein's E = mc^{2}, which takes the form E = \sqrt{m^{2} + p^{2}}, unifies the energy-momentum relations for massive and massless particles, but it does not take into account internal space-time structure of relativistic particles. It is pointed out Wigner's 1939 paper on the inhomogeneous Lorentz group defines particle spin and gauge degrees of freedom in the Lorentz-covariant world. Within the Wigner framework, it is shown possible to construct the internal space-time structure for hadrons in the quark model. It is then shown that the quark model and the parton model are two different manifestations of the same covariant entity. It is shown therefore that the lack of coherence in Feynman's parton picture is an effect of the Lorentz covariance.