Boost Generators: Physical Meaning & Observable Quantities

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SUMMARY

The discussion centers on the generators of the Poincare group, specifically focusing on boosts and their relationship to observable physical quantities. Time translations correspond to energy, space translations to momentum, and rotations to angular momentum. Boosts are linked to the relativistic angular momentum tensor, which unifies boosts and rotations, highlighting their frame-dependent nature. This understanding is crucial for comprehending the physical implications of boosts in relativistic physics.

PREREQUISITES
  • Understanding of the Poincare group in physics
  • Familiarity with relativistic angular momentum tensor
  • Knowledge of frame-dependent transformations in relativity
  • Basic concepts of energy, momentum, and angular momentum
NEXT STEPS
  • Research the Poincare group and its generators in quantum mechanics
  • Study the relativistic angular momentum tensor in detail
  • Explore the relationship between boosts and rotations in special relativity
  • Examine the implications of frame-dependent transformations in physical theories
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Physicists, students of theoretical physics, and anyone interested in the mathematical foundations of relativity and its observable consequences.

nicholas_eng
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TL;DR
Do the generators of boosts correspond to anything physical?
So, all of the generators of the Poincare group are associated with pretty well-known physical quantities. Time translation is associated with energy, space translations with momentum, rotations with angular momentum, and boosts... well, boosts are generated by the "generators of boosts". Do they correspond to any observable?
 
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A proper understanding of boosts in the context of your question requires unifying them with rotations; note that the split between what is a "boost" and what is a "rotation" is frame-dependent. When we unify boosts and rotations, we find that there is a relativistic angular momentum tensor that corresponds to the boost/rotation generators. Wikipedia has a brief discussion:

https://en.wikipedia.org/wiki/Relat...e_generator_of_spacetime_boosts_and_rotations
 
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