A Question on Density Tensors in General Relativity

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    Density Tensor
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SUMMARY

This discussion centers on the transformation rules of density tensors in General Relativity, specifically referencing Problem 7 from Gerard t'Hooft's exercises. The user expresses difficulty in understanding the material presented in Geroch's "Geometrical Quantum Mechanics," particularly in sections III and 14. The lack of clarity in tensor notation and transformation rules is a common challenge for learners in this field, indicating a need for more accessible resources or explanations.

PREREQUISITES
  • Understanding of General Relativity concepts
  • Familiarity with tensor notation and operations
  • Knowledge of density matrices and their applications
  • Basic grasp of quantum mechanics principles
NEXT STEPS
  • Study the transformation rules for tensors in General Relativity
  • Read Geroch's "Geometrical Quantum Mechanics" focusing on sections 14 and 15
  • Explore online resources or tutorials on tensor notation
  • Investigate supplementary texts on density matrices in quantum mechanics
USEFUL FOR

Students and researchers in physics, particularly those studying General Relativity and quantum mechanics, will benefit from this discussion as it addresses common challenges in understanding density tensors and their transformations.

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Homework Statement


this is a problem of exercise of general relativity by Gerard t Hooft

Problem 7, Transformation rule of a density
http://p13.freep.cn/p.aspx?u=v20_p13_photo_1211140612144629_0.jpg

sry i don't know how to type tensors with upper and lower indices. I can only show it by picture

Homework Equations



questions are in the picture

The Attempt at a Solution



I tried to read Geroch's "Geometrical Quantum Mechanics", (III Quantum Mechanics 14. Densities. Integrals. 15. States), but i still cannot understand it
 
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was i in a wrong section that nobody could help?
 

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