In particle and condensed matter physics, Nambu-Goldstone bosons are bosons that appear in models with spontaneously broken symmetry.

In certain supersymmetric models, "Goldstone fermions," or "Goldstinos" also appear. So do sgoldstinos. The simplest model 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

$\backslash lambda^2(\backslash phi^*\backslash phi\; -\; k^2)^2\; \backslash ,$

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

$\backslash phi\; =\; k\; e^\{i\backslash theta\}\; \backslash ,$

where θ is the Goldstone boson (actually kθ is) with the Lagrangian density given by:

$\{\backslash mathcal\; L\}=-\backslash frac\{1\}\{2\}(\backslash partial^\backslash mu\; \backslash phi^*)\backslash partial\_\backslash mu\; \backslash phi\; +m^2\; \backslash phi^*\; \backslash phi\; =\; -\backslash frac\{1\}\{2\}(-ik\; e^\{-i\backslash theta\}\; \backslash partial^\backslash mu\; \backslash theta)(ik\; e^\{i\backslash theta\}\; \backslash partial\_\backslash mu\; \backslash theta)\; +\; m^2\; k^2=-\backslash frac\{k^2\}\{2\}(\backslash partial^\backslash mu\; \backslash theta)(\backslash partial\_\backslash mu\; \backslash theta)\; +\; m^2\; k^2.$

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.

See also

• Goldstone's theorem
• Pseudo-Goldstone boson
• Majoron
• Higgs Boson

Bosons | Quantum field theory