Why is it interesting?

The scalar model in 1 spatial and 1 time dimension is the simplest quantum field theory we can study. It is often used to introduce the basics of solitonic solutions, since the Scalar 1+1 models contains a kink solution.

Layman

Student

The model only contains a real scalar field $\phi (x) \in \mathbb{R}$. The scalar potential is

$$ U= \frac{\lambda}{2} ( \phi^2-a^2)^2, $$

and is conveniently normalized such that the ground state (the vacuum solution) is at $U=0$. In addition, the potential is bounded from below $U\geq 0$.

The field equation is

$$ \partial_{x_i}^2 \phi = 2 \lambda \phi (\phi^2-a^2). $$

It is important to note that this field equation is a non-linear differential equation and hence allows non-linear solutions.

Solitonic Solutions - The Kink

Researcher

Examples

Example1

Example2:

FAQ

History