Interactions of Fermion & Scalar Fields: Exploring the Difference

In summary, the two interactions described, \mathrm{i} g \bar{\psi}\psi \varphi and \mathrm{i} g \bar{\psi}\gamma_5\psi\varphi, differ in their transformation properties under parity. The first is a scalar coupling, while the second is a pseudoscalar coupling. This distinction is important in understanding the physical differences between these interactions, particularly in the context of the weak force which couples only to left-handed fields. The symmetries of the interactions also play a role in determining their use in modeling different physical phenomena.
  • #1
jdstokes
523
1
Suppose I couple a fermion field to a scalar field using [itex]\mathrm{i} g \bar{\psi}\psi \varphi [/itex] and [itex]\mathrm{i} g \bar{\psi}\gamma_5\psi\varphi[/itex].

I'm trying to understand what would be the physical difference between these interactions. I know that [itex](1/2)(1\pm \gamma_5)[/itex] approximately projects out the left and right handed components of Dirac fields and that this is related to the fact that the weak interaction couples preferentially to left-handed particles and right-handed anti-particles, but other than that I'm pretty clueless.
 
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  • #2
Your first interaction lagrangian is a scalar coupling, while the second is a pseudoscalar coupling. Check how they both transform under parity.
 
  • #3
What is the physical difference in the interactions apart from their transformation properties?
 
  • #4
The symmetries of the interaction define what interactions they are used to model.
 
  • #5
jdstokes said:
Suppose I couple a fermion field to a scalar field using [itex]\mathrm{i} g \bar{\psi}\psi \varphi [/itex] and [itex]\mathrm{i} g \bar{\psi}\gamma_5\psi\varphi[/itex].

I'm trying to understand what would be the physical difference between these interactions. I know that [itex](1/2)(1\pm \gamma_5)[/itex] approximately projects out the left and right handed components of Dirac fields and that this is related to the fact that the weak interaction couples preferentially to left-handed particles and right-handed anti-particles, but other than that I'm pretty clueless.

The weak force not only prefers left-handed; at tree level there is no weak coupling to right-handed fields.

The weak force is slightly more complicated than your model because vector bosons are vectors (duh). You can write the weak coupling as a sum of alpha*Vector + beta*Axial Vector couplings. Up to an internal minus sign (always mix it up), the weak coupling is pure V+A, so it couples solely to left-handed fields. The most obvious physical observable used to demonstrate this is the polarized e+/e- beam experiment of SLD...
 

1. What is the difference between fermion and scalar fields?

Fermion fields are quantum fields that describe particles with half-integer spin, such as electrons, protons, and neutrons. Scalar fields, on the other hand, describe particles with integer spin, such as the Higgs boson. The main difference between the two is the spin of the particles they describe, which has important implications for their behavior and interactions.

2. How do fermion and scalar fields interact with each other?

Fermion and scalar fields can interact through a process called Yukawa coupling, where a fermion particle exchanges virtual scalar particles with another fermion particle. This interaction is responsible for giving particles mass through the Higgs mechanism.

3. What experimental evidence supports the existence of fermion and scalar fields?

The Standard Model of particle physics, which is the most widely accepted theory describing the fundamental particles and forces of the universe, includes both fermion and scalar fields. These fields have also been indirectly observed through experiments such as the Large Hadron Collider, where the Higgs boson was discovered in 2012.

4. Can fermion and scalar fields be unified into a single theory?

Many theories, such as supersymmetry, attempt to unify fermion and scalar fields into a single framework. However, these theories have not yet been experimentally confirmed and are still a subject of ongoing research in the field of particle physics.

5. How do interactions between fermion and scalar fields contribute to our understanding of the universe?

Studying the interactions between fermion and scalar fields helps us understand the fundamental forces and building blocks of the universe. These interactions play a crucial role in processes such as particle decay and the formation of matter, and studying them can provide insights into the origins of the universe and its evolution.

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