Generalized Dirac Equation for All Fermions?

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Discussion Overview

The discussion centers around the existence of a "Generalized Dirac Equation" that could apply to all fermions, not limited to those of spin 1/2. Participants explore the theoretical framework and experimental validation related to fermions of various spins, including spin-3/2 and higher spins.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire whether a Generalized Dirac Equation has been experimentally validated for all fermions beyond spin 1/2.
  • Others mention that current theories primarily involve fundamental fermions of spin-1/2 and spin-3/2, with higher-spin fermions not being utilized in practice.
  • A participant notes that the Rarita-Schwinger equation serves as the equivalent for spin-3/2 particles but questions the existence of a general equation for all half-integer spins.
  • It is proposed that specific equations can be formulated for particular spin values, referencing Weinberg's work in quantum field theory.
  • Concerns are raised about the experimental feasibility of higher-spin fermions, with a participant stating that no gravitino has been observed and suggesting limitations on the existence of higher-spin particles.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the existence of a generalized equation applicable to all fermions, with multiple competing views on the theoretical and experimental aspects of higher-spin fermions. The discussion remains unresolved.

Contextual Notes

Limitations include the lack of experimental evidence for higher-spin fermions and the dependence on theoretical frameworks that may not encompass all possible spin values.

LarryS
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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.
 
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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.
 
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.
 
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).
 
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.
 

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