Goldstone boson
|
|
In particle physics, Goldstone bosons are bosons that appear in models with spontaneously broken symmetry.
In certain supersymmetric models, "Goldstone fermions," or "Goldstinos" also appear.
The simplest model (almost trivial) with a Goldstone boson is as follows:
We have a complex scalar field φ (phi), with the constraint that φ*φ=k2. One way to get a constraint of that sort is by including a potential
- <math>\lambda^2(\phi^*\phi - k^2)^2 \,<math>
and taking the limit as λ goes to infinity. The field can be redefined to give a real scalar, θ, without a constraint by using
- <math>\phi = k e^{i\theta} \,<math>
where θ is the Goldstone boson (actually kθ is) with the Lagrangian density given by:
- <math>L=-\frac{1}{2}(\partial^\mu \phi^*)\partial_\mu \phi +m^2 \phi^* \phi = -\frac{1}{2}(-ik e^{-i\theta} \partial^\mu \theta)(ik e^{i\theta} \partial_\mu \theta) + m^2 k^2=-\frac{k^2}{2}(\partial^\mu \theta)(\partial_\mu \theta) + m^2 k^2.<math>
Note that the constant term m2k2 has no physical significance and the other term is simply the kinetic term for a massless scalar. In general the Goldstone boson is always massless, and parametrises the curve of possible vacuum states.
A somewhat simpler but more detailed presentation of the same concepts is presented in the article on the Yukawa interaction.