Lagrangian for a supersymmetric point particle

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SUMMARY

The Lagrangian for a supersymmetric point particle is expressed as S = \frac{1}{2} \int \frac{d\tau}{e}[\dot{X}^2 +i \dot{\psi}{\psi}-2ie\nu \dot{X} \psi], where e represents the graviton and ν denotes the gravitino. This formulation is crucial for deriving the worldsheet Lagrangian in superstring theory. A reliable reference for this Lagrangian can be found in problem 4.1 of the book by Becker, Becker, and Schwarz. Verification of the constants in the Lagrangian can be achieved by solving the equations of motion.

PREREQUISITES
  • Understanding of supersymmetry concepts
  • Familiarity with Lagrangian mechanics
  • Knowledge of superstring theory fundamentals
  • Ability to solve equations of motion in theoretical physics
NEXT STEPS
  • Research the derivation of the worldsheet Lagrangian in superstring theory
  • Study the equations of motion for the given Lagrangian
  • Explore the role of gravitons and gravitinos in supersymmetry
  • Read Becker, Becker, and Schwarz for detailed insights on supersymmetric theories
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The discussion is beneficial for theoretical physicists, particularly those specializing in supersymmetry and superstring theory, as well as students seeking to deepen their understanding of Lagrangian formulations in advanced physics.

jdstokes
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Does anyone know where I can find the lagrangian for this?

From memory I believe it looks something like

S = \frac{1}{2} \int \frac{d\tau}{e}[\dot{X}^2 +i \dot{\psi}{\psi}-2ie\nu \dot{X} \psi]

where e is the graviton and nu is the gravitino. Does anyone know of a reference that supports this?
 
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That looks correct to me up to constants in front of each term. If you solve the eom you could verify that the constants are correct or not.
 
Hi Haelfix,

Thanks for your response. I do not have the equations of motion handy so I was hoping someone might know of a reference which discusses this.

I believe this Lagrangian can be used to motivate the worldsheet Lagrangian in superstring theory.
 
For future reference, the answer can be found in problem 4.1 of Becker, Becker and Shwarz.
 

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