# Coupling fermions to a scalar field: Interpretation problem

• blue2script
In summary, the conversation is discussing the coupling of a fermion to a 2D scalar O(3) model and the interpretation of the Lagrangian formula. The participants are asking for clarification on the role of the gauge field and the physical significance of the scalar model. The scalar field could potentially have a role in explaining inflation.
blue2script
Hi all,

I have a little problem concerning the coupling of a fermion to CP^N (or better a 2D scalar O(3) model). Its not a mathematical type of problem. I just read on

"The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions"

http://arxiv.org/PS_cache/hep-th/pdf/0402/0402013v2.pdf

The Lagrangian of this theory is written down in (2.1) and I am a bit lost as of interpreting this formula. There are three indegredients: 1. a scalar field, 2. a fermionic field and 3. a gauge field. Now, a scalar field represents a spin-0 field, right? The fermionic field is of spin 1/2. But now what is the gauge field? The scalar field may have some internal symmetry like O(3) but this won't affect the Lagrangian. I just don't understand what the gauge field is in this case.

Could somebody explain that to me? A big thanks in advance!

Blue2script

PS: Also, of what physical interest is the scalar model besides being a nice toy model to study field effects? What could be the interpretation of a scalar field?

For example, in a chiral supermultiplet, you can have a scalar field and Weyl fermion fields in the same supermultiplet.

Such scalar fields are candidates for the inflaton field that led to inflation (the Higgs doesn't quite work as that field).

## 1. What is the interpretation problem when coupling fermions to a scalar field?

The interpretation problem arises when trying to understand the physical meaning of coupling fermions, which are particles with half-integer spin, to a scalar field, which has spin 0. This coupling violates the spin statistics theorem, which states that particles with half-integer spin must have anti-commuting (fermionic) fields, while particles with integer spin must have commuting (bosonic) fields.

## 2. Why is it important to study the coupling of fermions to a scalar field?

Studying the coupling of fermions to a scalar field is important because it has implications for our understanding of particle physics and the fundamental laws of nature. It also has potential applications in fields such as quantum field theory, cosmology, and condensed matter physics.

## 3. What are some proposed solutions to the interpretation problem?

There are several proposed solutions to the interpretation problem, including the idea of supersymmetry, which posits the existence of an additional symmetry between fermions and bosons. Other proposed solutions include the concept of non-locality and the possibility of emergent particles.

## 4. How does the interpretation problem affect our understanding of the universe?

The interpretation problem challenges our current understanding of the universe and the laws of physics. It raises questions about the fundamental nature of particles and their interactions, and may lead to new theories that could better explain the behavior of matter and energy in the universe.

## 5. What are some current research efforts focused on the interpretation problem?

Currently, there are ongoing research efforts to further explore and understand the interpretation problem. This includes theoretical studies using mathematical frameworks, as well as experimental efforts to observe the effects of coupling fermions to a scalar field in particle accelerators and other high-energy experiments.

• Quantum Physics
Replies
4
Views
936
• Cosmology
Replies
20
Views
1K
• High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
• Quantum Interpretations and Foundations
Replies
21
Views
2K
• Beyond the Standard Models
Replies
4
Views
2K
• Beyond the Standard Models
Replies
7
Views
2K
• Beyond the Standard Models
Replies
2
Views
798
• High Energy, Nuclear, Particle Physics
Replies
2
Views
2K
• Quantum Physics
Replies
24
Views
2K
• Cosmology
Replies
1
Views
1K