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Interplay between Mathematics and Physics

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If you have a question about this talk, please contact Mustapha Amrani.

Mathematics for the Fluid Earth

Co-author: Tian Ma (Sichuan University)

In this talk, we shall present three first principles and a few examples, demonstrating the symbiotic interplay between theoretical physics and advanced mathematics.

We start with a general principle that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. We shall illustrate this principle with a few examples in both equilibrium and non-equilibrium phase transitions, including the metastable oscillation mechanism of the El Nino Southern Oscillation (ENSO) and the existence of 3rd-order transitions beyond the Andrews critical point.

Then we present two basic principles: the principle of interaction dynamics (PID) and the principle of representation invariance (PRI), to study the nature’s fundamental interactions/forces. Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint. PRI requires that physical laws be independent of representations of the gauge groups. These two principles give rise to a unified field model for four interactions, which can be naturally decoupled to study individual interactions. With PID , for example, we derive new gravitational field equations with a vector field $Phi_mu$, which can be considered as a spin-1 massless bosonic particle field. The field equations induce a natural duality between the graviton (spin-2 massless bosonic particle) and this spin-1 massless bosonic particle, leading to a unified theory for dark matter and dark energy. In addition, the PID offers a completely different and much simpler way of introducing Higgs fields.

This talk is part of the Isaac Newton Institute Seminar Series series.

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