Understanding Composite Fields and Scalar Fields

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Discussion Overview

The discussion revolves around the nature of composite fields, specifically the product of Dirac spinors, denoted as psi_bar psi, and its classification as a scalar field. Participants explore the implications of this classification in the context of symmetry breaking and the Goldstone theorem, as well as the potential for massive particles to form massless bound states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the composite field psi_bar psi can be considered equivalent to a scalar field in all respects.
  • Another participant asserts that psi_bar psi is indeed a scalar field, being the simplest Lorentz scalar constructed from the Dirac spinor.
  • A further contribution discusses the implications of fermion-antifermion pairs generating a condensate, suggesting that this leads to a reduction in symmetry and raises questions about the application of the Goldstone theorem, particularly regarding translational invariance and singularities in the composite field.
  • A separate question is posed about the possibility of massive particles forming massless bound states, indicating an interest in the relationship between mass and binding in particle physics.

Areas of Agreement / Disagreement

Participants express differing views on the classification of psi_bar psi as a scalar field, with some asserting its scalar nature while others raise concerns about its properties in the context of symmetry breaking and the Goldstone theorem. The discussion remains unresolved regarding the implications of these points.

Contextual Notes

There are limitations regarding the assumptions made about translational invariance and the treatment of singularities in composite fields, which are not fully resolved in the discussion.

Neitrino
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Dear PF,

Can I consider the composite field for instance psi_bar psi as a scalar filed?
I mean can it be the same in all respects? Can this composite field and scalar filed treated as totally equivalent?

Thks
 
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Well it is a scalar field. [itex]\bar{\psi}\psi[/itex] is the simplest Lorentz scalar one can construct from the Dirac spinor [itex]\psi[/itex].
 
Suppose I have only fermions and due to some reason fermion-antifermion pairs generate condensate condensate, so SU(N)left*SU(N)right symmetry reduced to SU(N)diag symmetry. Here one says that due to Goldstone theorem there should emerge massles Goldstone bosons. But in proof of goldstone theorem the translation invariance is very essential... so if I treat psi_bar psi as a scalar composed from dirak spinors then this scalar has singularity because product of local operators can have singularities. Making point splitting psi(x+epsilon)psi_bar (x-epsilon) we avoid singularty, but lose translational invariance which is very essential in proof of Goldstone theorem, so in fermion field symmetry breaking Goldstone theorem is no defined well? so psi_bar psi is no "good" scalar filed ?
 
just another question - can massive particles form massles bound state?
 

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