Generalized Dirac Equation for All Fermions?

In summary, there is no generalized Dirac Equation that has been experimentally proven to work for all fermions. The only fundamental fermions currently used in theories are spin-1/2 and spin-3/2. While there is a Rarita-Schwinger equation for spin-3/2 particles, it is not clear if there is a general equation to cover all half-integer spins. In string theory, there are infinite towers of fields with increasing spin, but they have not yet been observed experimentally.
  • #1
LarryS
Gold Member
354
33
The original Dirac Equation was for the electron, a particle of spin 1/2.

Is there a "Generalized Dirac Equation" that has been experimentally proven to work for all fermions, not just those of spin 1/2?

Thanks in advance.
 
Physics news on Phys.org
  • #2
referframe said:
The original Dirac Equation was for the electron, a particle of spin 1/2.

Is there a "Generalized Dirac Equation" that has been experimentally proven to work for all fermions, not just those of spin 1/2?

Thanks in advance.

I don't have an answer, but I thought it was the case that the only fundamental fermions appearing in any current theory is spin-1/2 and spin-3/2 (which appears in supergravity). Higher-spin fermions are not used for anything, as far as I know. Of course, a composite particle can have an arbitrarily large spin.
 
  • #3
The equivalent equation for spin-3/2 particles is the Rarita-Schwinger equation. I don't know if there is any sort of general equation to cover all half-integer spins.
 
  • #4
It can be done for any particular value of the spin; Weinberg's QFT vol.1 explains how, in general, this works. Also, in string theory, you get infinite towers of fields with increasing spin (and mass).
 
  • #5
The experimental part is an issue, there's no gravitino except on paper so far. Spin 5/2, 7/2, ... can't exist on paper, apparently, even though the general spin wave equation is as old as 1936 and the article by Dirac in PRSL. Then Pauli + Fierz, Bhabha, Duffin + Kemmer and last but not least Gel'fand and Yaglom.
 

FAQ: Generalized Dirac Equation for All Fermions?

What is the Generalized Dirac Equation for All Fermions?

The Generalized Dirac Equation for All Fermions is a mathematical equation that describes the behavior of fermions, which are particles with half-integer spin, in a relativistic quantum field theory. It is an extension of the original Dirac equation, which only applies to electrons, to encompass all other types of fermions such as quarks, neutrinos, and muons.

How does the Generalized Dirac Equation for All Fermions differ from the original Dirac equation?

The Generalized Dirac Equation for All Fermions takes into account the different properties of various fermions, such as their mass and charge, while the original Dirac equation only applies to electrons. It also includes additional terms to account for interactions between different types of fermions.

What is the significance of the Generalized Dirac Equation for All Fermions in the field of particle physics?

The Generalized Dirac Equation for All Fermions is a fundamental equation in the field of particle physics as it provides a unified description of all known fermions and their interactions. It has been extensively used in the development of the Standard Model, which is the current theory that explains the behavior of particles and their interactions.

Can the Generalized Dirac Equation for All Fermions be used to predict the existence of new particles?

Yes, the Generalized Dirac Equation for All Fermions has been successful in predicting the existence of new particles, such as the charm quark and the tau neutrino. By applying the equation to different scenarios and experiments, scientists can make predictions about the properties of undiscovered particles.

Are there any current challenges or limitations in using the Generalized Dirac Equation for All Fermions?

One of the main challenges in using the Generalized Dirac Equation for All Fermions is its complexity and the need for advanced mathematical techniques to solve it. Another limitation is that it does not take into account the effects of gravity, which is a major aspect of the universe. Efforts are currently being made to develop a more comprehensive theory that can incorporate both particle interactions and gravity.

Similar threads

I The components of Dirac Equation -- Bosonic Lagrangian?
Replies
8
Views
891
I The Dirac equation as a linear tensor equation for one component
Replies
0
Views
690
I Understanding the Equations of Motion for the Dirac Lagrangian
Replies
1
Views
2K
I Matrix elements of Hamiltonian include Dirac delta term
Replies
2
Views
750
I General Concepts About Fermi-Dirac Distribution
Replies
8
Views
1K
I What do the psi_3 and psi_4 components of the Dirac equation represent?
Replies
8
Views
2K
A Effective Action for Scalar and Fermion Fields
Replies
4
Views
1K
I Why does the Dirac equation lead to spin 1/2?
Replies
8
Views
6K
I Why is the SE better than the KG equation for a hydrogen atom?
Replies
18
Views
2K
I Spin conservation in the Dirac equation
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top