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SUMMARY:Interplay between Mathematics and Physics - Wang\, S (Indiana Univ
 ersity)
DTSTART:20131029T114500Z
DTEND:20131029T122000Z
UID:TALK48548@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Tian Ma (Sichuan University)\n\nIn this talk\, we s
 hall present three first principles and a few examples\, demonstrating the
  symbiotic interplay between theoretical physics and advanced mathematics.
 \n\nWe start with a general principle that dynamic transitions of all diss
 ipative systems can be classified into three categories: continuous\, cata
 strophic and random. We shall illustrate this principle with a few example
 s in both equilibrium and non-equilibrium phase transitions\, including th
 e metastable oscillation mechanism of the El Nino Southern Oscillation (EN
 SO) and the existence of 3rd-order transitions beyond the Andrews critical
  point.\n\nThen we present two basic principles: the principle of interact
 ion dynamics (PID) and the principle of representation invariance (PRI)\, 
 to study the nature's fundamental interactions/forces. Intuitively\, PID t
 akes the variation of the action functional under energy-momentum conserva
 tion constraint. PRI requires that physical laws be independent of represe
 ntations of the gauge groups. These two principles give rise to a unified 
 field model for four interactions\, which can be naturally decoupled to st
 udy individual interactions. With PID\, for example\, we derive new gravit
 ational field equations with a vector field $Phi_mu$\, which can be consid
 ered as a spin-1 massless bosonic particle field. The field equations indu
 ce a natural duality between the graviton (spin-2 massless bosonic particl
 e) and this spin-1 massless bosonic particle\, leading to a unified theory
  for dark matter and dark energy. In addition\, the PID offers a completel
 y different and much simpler way of introducing Higgs fields.\n
LOCATION:Seminar Room 1\, Newton Institute
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