Representations of the Lorentz group

In summary, the conversation is about recommendations for literature on representations of the Lorentz group, specifically in relation to the Dirac equation. The poster is looking for a deeper understanding and someone named Sam has provided helpful information on the topic. A book by Wu Ki Tung on group theory with applications in physics is suggested as a good resource for those interested in learning more without extensive mathematical knowledge.
  • #1
center o bass
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Can anyone recommend some litterature on representations of the Lorentz group. I'm reading about the dirac equation and there the spinor representation is used, but I would very much like to get a deeper understanding on what is going on.
 
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  • #3
This is a very broad subeject and even whole books have been written about it. Indeed, Sam gave there a brilliant summary of results and if you're interested in more without delving into hard mathematics, then the book by Wu Ki Tung on group theory with applications in physics would be an appropriate choice.
 

1. What is the Lorentz group?

The Lorentz group is a mathematical group that describes the transformations between reference frames in physics. It is named after the Dutch physicist Hendrik Lorentz and is an essential component of Albert Einstein's theory of special relativity.

2. How is the Lorentz group represented?

The Lorentz group is represented by a set of 4x4 matrices, known as Lorentz transformations, that describe how physical quantities such as space and time coordinates change when moving between reference frames. These transformations include rotations, boosts, and combinations of both.

3. What is the significance of the Lorentz group in physics?

The Lorentz group is crucial in physics because it describes the fundamental principle of relativity, which states that the laws of physics should be the same for all observers moving at a constant velocity. It also plays a central role in the study of high-energy physics and the behavior of particles at relativistic speeds.

4. How is the Lorentz group related to the concept of spacetime?

The Lorentz group is closely related to the concept of spacetime, which combines the three dimensions of space with the dimension of time into a four-dimensional continuum. The Lorentz transformations describe how spacetime coordinates change when moving between frames of reference, and are essential for understanding the effects of relativity on the geometry of spacetime.

5. Are there any applications of the Lorentz group outside of physics?

While the Lorentz group is primarily used in physics, it also has applications in other fields such as engineering, computer graphics, and robotics. It is used to model the motion of objects, including spacecraft and robots, and to calculate the effects of relativistic speeds on these objects. Additionally, the mathematics of the Lorentz group has implications in other areas of mathematics, such as Lie algebra and representation theory.

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