Dirac equation for electron in EM and Higgs fields?

In summary, the Dirac equation is a fundamental equation in quantum field theory that describes the behavior of spin-1/2 particles, such as electrons, in the presence of both electromagnetic and Higgs fields. It includes a term for the electron's intrinsic spin and accounts for the interactions between the electron's spin and the electromagnetic field. The Higgs field, represented by the Higgs potential, affects the electron's behavior by generating a mass term in the equation. The Dirac equation is a cornerstone of modern physics and has been crucial in explaining and predicting the behavior of particles at the subatomic level, as well as understanding matter in extreme environments.
  • #1
johne1618
371
0
Is this the correct form for a Dirac electron in a Higgs field with scalar potential [itex]\phi[/itex] and an electromagnetic field with vector potential [itex]A_\mu[/itex]

[itex]i \gamma^\mu \partial_\mu \psi = g \phi \psi + e \gamma_\mu A^\mu \psi [/itex]

where [itex]g[/itex] is the coupling constant to the Higgs field and [itex]e[/itex] is the coupling constant to the electromagnetic field?
 
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  • #3
Bill_K said:
Looks Ok to me. And φ = v + h.

Thanks a lot.

I guess v is the Higgs vacuum expectation value and h is the physical Higgs field.
 

1. What is the Dirac equation for an electron in electromagnetic and Higgs fields?

The Dirac equation is a relativistic wave equation that describes the behavior of spin-1/2 particles, such as electrons, in the presence of both electromagnetic and Higgs fields. It was first proposed by physicist Paul Dirac in 1928 and is a fundamental equation in quantum field theory.

2. How does the Dirac equation account for the electron's spin?

The Dirac equation includes a term that describes the electron's intrinsic spin, which is a property of particles at the quantum level. This term allows the equation to accurately predict the behavior of electrons in experiments, such as the Stern-Gerlach experiment, which demonstrated the existence of spin.

3. What is the role of the electromagnetic field in the Dirac equation?

The electromagnetic field is represented in the Dirac equation by the vector potential, which describes the strength and direction of the electric and magnetic fields in the presence of charged particles like electrons. The equation takes into account the interactions between the electron's spin and the electromagnetic field, allowing us to understand how the electron responds to changing electric and magnetic fields.

4. How does the Higgs field affect the behavior of electrons described by the Dirac equation?

The Higgs field, which is responsible for giving particles their mass, is represented in the Dirac equation by the Higgs potential. This potential interacts with the electron's spin, generating a mass term in the equation that accounts for the electron's mass and how it interacts with other particles in the Higgs field.

5. What are the implications of the Dirac equation for modern physics?

The Dirac equation, along with the principles of quantum mechanics and special relativity, is a cornerstone of modern physics. It has been used to explain and predict the behavior of particles at the subatomic level, and has led to the development of important theories such as quantum electrodynamics. The equation is also crucial in understanding the behavior of matter in extreme environments, such as in particle accelerators or the early universe.

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