Understanding Physics with a Rank 4 Tensor Example

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SUMMARY

The discussion centers on the identification of rank 4 tensors in physics, specifically highlighting the Riemann curvature tensor (Rijkl) utilized in general relativity and the third-order nonlinear susceptibility as another example. These tensors play crucial roles in advanced physics, particularly in the context of gravitational theories and material science. The conversation emphasizes the importance of understanding higher-order tensors beyond the commonly studied rank 3 tensors.

PREREQUISITES
  • Understanding of tensor mathematics
  • Familiarity with general relativity concepts
  • Knowledge of nonlinear optics
  • Basic grasp of curvature in differential geometry
NEXT STEPS
  • Study the properties and applications of the Riemann curvature tensor in general relativity
  • Explore the concept of third-order nonlinear susceptibility in material science
  • Learn about tensor calculus and its applications in physics
  • Investigate the role of higher-order tensors in advanced theoretical frameworks
USEFUL FOR

Students of physics, researchers in general relativity, and professionals in material science seeking to deepen their understanding of tensor applications in complex systems.

SteDolan
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Hi,

Can somebody give me an example of a rank 4 tensor in physics?

Thanks.
 
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Sure, one would be the Riemann curvature tensor Rijkl that's used in general relativity.
 
Thanks.

It was an odd small part of an exam question when my module had only covered examples up to 3rd rank.
 
Third order nonlinear susceptibility is another example of 4th rank tensor.
 

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