Poincare Transformation: Understanding its Properties and Group Structure

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SUMMARY

The Poincare transformation is established as a noncompact Lie group characterized by properties such as associativity, closure, identity element, and inversion element. Saeede initiated the discussion seeking guidance on proving these properties, while Tom suggested starting with the proof of the Poincare Algebra, which Saeede found to be simpler than anticipated. This foundational understanding is crucial for further exploration of the group's structure.

PREREQUISITES
  • Understanding of Lie groups and their properties
  • Familiarity with algebraic structures, specifically groups
  • Basic knowledge of Poincare transformations
  • Experience with mathematical proofs and theorems
NEXT STEPS
  • Study the proof of the Poincare Algebra in detail
  • Explore the implications of noncompact Lie groups in physics
  • Research the applications of Poincare transformations in relativity
  • Examine the relationship between Poincare transformations and symmetry in quantum mechanics
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, and students interested in advanced algebraic structures, particularly those studying the foundations of theoretical physics and the mathematical underpinnings of relativity.

Saeide
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Dear all,

Poincare transformation construct a group, better to say noncompact Lie group. I want to prove this fact but I don't know how...; I mean the general characteristics- associativity, closure, identity element and inversion element.
I would appreciate it if anyone could help me or guide me to references in this topic.
So thanks in advance,


Saeede
 
Physics news on Phys.org
What about - as a first step - a proof of the Poincare Algebra?
 
Well I found how to prove it; That was so simpler than what I really thought! By the way I'm so thankful for your attention Tom. I will go for the Poincare algebra as the next step!
 

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