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Solutions in Classical Field Theory

Vejleder: Thomas Ryttov


Exact solutions to the Euler-Lagrange equations of motion are hard to come by in classical field theory. A first attempt at understanding the theory might be to solve the equations order by order in perturbation theory. First the project can briefly discuss perturbation theory as a method of finding solutions to the field equations in scalar field theory. Naturally this will also include the shortcomings of perturbation theory.

The project can then proceed to introduce the Sine-Gordon theory and/or the Korteweg-de Vries (KdV) theory in 1+1 dimensions. Here solitonic solutions to the field equations can be discussed including the scattering of solitons off one another. One can then contrast these non-perturbative solutions to standard solutions found via perturbatiion theory. It is also possible to discuss the structure of conserved charges.

Lastly, if time permits, the project can introduce Abelian and non-Abelian gauge fields and their coupling to scalar fields. This could then pave the way for a study of the ’t Hooft – Polyakov monopole solution in the Georgi-Glashow model. Understanding non-perturbative phenomena are crucial in order to get to the cutting edge of modern theoretical physics.

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Sidst opdateret: 09.09.2021