Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation

Details Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation

2003-06-27

arxiv.org/abs/hep-th/0306275v1

J.Math.Phys.44:2839,2003

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, no figures

Scientific paper

10.1063/1.1576907

We analyze the group-theoretical ramifications of the Nambu-Goldstone [NG] theorem in the self-consistent relativistic variational Gaussian wave functional approximation to spinless field theories. In an illustrative example we show how the Nambu-Goldstone theorem would work in the O(N) symmetric $\phi^4$ scalar field theory, if the residual symmetry of the vacuum were lesser than O(N-1), e.g. if the vacuum were O(N-2), or O(N-3),... symmetric. [This does not imply that any of the "lesser" vacua is actually the absolute energy minimum: stability analysis has not been done.] The requisite number of NG bosons would be (2N - 3), or (3N - 6), ... respectively, which may exceed N, the number of elementary fields in the Lagrangian. We show how the requisite new NG bosons would appear even in channels that do not carry the same quantum numbers as one of N "elementary particles" (scalar field quanta, or Castillejo-Dalitz-Dyson [CDD] poles) in the Lagrangian, i.e. in those "flavour" channels that have no CDD poles. The corresponding Nambu-Goldstone bosons are composites (bound states) of pairs of massive elementary (CDD) scalar fields excitations. As a nontrivial example of this method we apply it to the physically more interesting 't Hooft $\sigma$ model (an extended $N_{f} = 2$ bosonic linear $\sigma$ model with four scalar and four pseudoscalar fields), with spontaneously and explicitly broken chiral $O(4) \times O(2) \simeq SU_{\rm R} (2) \times SU_{\rm L}(2) \times U_{\rm A}(1)$ symmetry.

Affiliated with

Also associated with

No associations

Rating

Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-335385