Deriving commutator of operators in Lorentz algebra

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SUMMARY

The discussion focuses on deriving the commutator of operators in the Lorentz algebra, specifically the expression [Li, Lj] = i∈ijkLk. The operators are defined as Li = 1/2*∈ijkJjk and Ki = J0i, with J satisfying the Lorentz commutation relation. The user seeks clarification on how to transform the initial expression into the desired commutator form, referencing a specific physics document for additional context.

PREREQUISITES
  • Understanding of Lorentz algebra and its commutation relations
  • Familiarity with tensor notation and Levi-Civita symbols
  • Knowledge of quantum mechanics and operator algebra
  • Basic proficiency in mathematical physics
NEXT STEPS
  • Study the derivation of commutation relations in quantum mechanics
  • Explore the properties of the Levi-Civita symbol in tensor calculus
  • Review the structure of the Lorentz group and its representations
  • Investigate applications of Lorentz algebra in particle physics
USEFUL FOR

This discussion is beneficial for theoretical physicists, graduate students in quantum mechanics, and researchers focusing on the Lorentz group and its applications in high-energy physics.

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Homework Statement
How to derive the commutator of L and K according to the Lorentz commutation relations.
Relevant Equations
see below
Li=1/2*∈ijkJjk, Ki=J0i,where J satisfy the Lorentz commutation relation.
[Li,Lj]=i/4*∈iabjcd(gbcJad-gacJbd-gbdJac+gadJbc)
How can I obtain
[Li,Lj]=i∈ijkLk
from it?
 
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Is this any help?

http://www.physics.mcgill.ca/~guymoore/ph551/appendixC.pdf
 
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