Understanding Composite Fields and Scalar Fields

In summary, The composite field \bar{\psi}\psi can be considered as a scalar field, and it is equivalent to a Lorentz scalar constructed from the Dirac spinor \psi. However, there may be issues with treating it as a scalar due to singularities in the product of local operators. In the context of fermion field symmetry breaking, the Goldstone theorem may not be well-defined when using the composite field \bar{\psi}\psi. Additionally, it is possible for massive particles to form massless bound states.
  • #1
Neitrino
137
0
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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  • #2
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].
 
  • #3
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 ?
 
  • #4
just another question - can massive particles form massles bound state?
 

FAQ: Understanding Composite Fields and Scalar Fields

What is the difference between a composite field and a scalar field?

A composite field is a vector field that is made up of multiple scalar fields. This means that each point in the field has multiple scalar values that describe its properties. On the other hand, a scalar field is a field that has only one scalar value at each point, representing a single physical quantity.

How are composite fields and scalar fields used in science?

Composite fields and scalar fields are used in various fields of science, such as physics, engineering, and biology. They are used to describe and analyze physical phenomena, such as electric and magnetic fields, fluid flow, and temperature distribution.

What are some examples of composite fields and scalar fields?

Some examples of composite fields include the electric field, which is made up of the electric potential and the electric charge density, and the magnetic field, which is made up of the magnetic flux density and the magnetic field strength. Some examples of scalar fields include temperature fields, pressure fields, and concentration fields.

How are composite fields and scalar fields represented and visualized?

Composite fields and scalar fields can be represented and visualized using mathematical equations and vector or contour plots. These plots show the variation of the field values over a specific region, allowing scientists to analyze and understand the behavior of the field.

What are some real-world applications of understanding composite fields and scalar fields?

Understanding composite fields and scalar fields is crucial in many real-world applications. For example, in engineering, they are used to design and optimize structures and systems, such as aerodynamics in aircrafts. In biology, they are used to study fluid flow in the cardiovascular system. In physics, they are used to analyze the behavior of particles in electromagnetic fields.

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