The Poincare Group: A Study of Second Part of 3.26 and 3.27

In summary, the conversation starts with someone asking for help understanding a section about the Poincare group in a book. They are specifically confused about how the second part of (3.26 and 3.27) follows from the first part and request the actual formulas they are asking about. Another person suggests looking at their lecture notes on qft for more information.
  • #1
Caloric
3
0
Hi all!

I'm trying to study the Poincare group and I have one problem. I'm reading a book: Gross D. Lectures on Quantum Field Theory (there is section about it). So I do not understand how the second part of (3.26 and 3.27) folows from the first part i.e I do not understand how was obtained the commutator.
 
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  • #2
I don't know why a lot of people assume that everyone here has every single physics book ever written. Can you, maybe, provide the actual formulas you are asking a question about? That dramatically increases the odds that somebody will help you out.
 
  • #3
Good point. I'd like to help, but have no access to this book now. For the time being, you may have a look at my lecture notes on qft, where you find a lot on the Poincare group and its representations,

http://fias.uni-frankfurt.de/~hees/publ/lect.pdf
 

1. What is the Poincare Group?

The Poincare Group is a mathematical concept that describes the symmetries of physical systems in spacetime. It combines the principles of special relativity and the laws of conservation of energy and momentum, and is used to study the dynamics of particles and fields in physics.

2. How is the Poincare Group related to 3.26 and 3.27?

3.26 and 3.27 refer to specific sections in a mathematical text that discuss the Poincare Group. In these sections, the group is defined and its properties and applications are explored in depth.

3. What are the components of the Poincare Group?

The Poincare Group is made up of four components: translations in space and time, rotations in space, boosts (or velocity transformations), and the identity component. These components form the basis for studying the symmetries and transformations of physical systems.

4. How is the Poincare Group used in physics?

The Poincare Group is used in physics to study the behavior of particles and fields in spacetime. It allows for the calculation of physical quantities such as energy, momentum, and angular momentum, and is essential for understanding the fundamental laws of nature such as the conservation of energy and momentum.

5. What are some real-world applications of the Poincare Group?

The Poincare Group has many real-world applications in physics, including in the study of particle physics, quantum mechanics, and general relativity. It is also used in the development of technologies such as GPS and in the analysis of high-energy collisions in particle accelerators.

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