Regarding representations of the Lorentz group

In summary, on page 38 of Peskin and Schroeder, it is stated that the most general nonlinear transformation laws can be derived from linear transformations. Therefore, there is no need to consider transformations that are more general. The specific transformation mentioned is \Phi_a(x) \rightarrow M_{ab}(\Lambda)\Phi_b(\Lambda^{-1}x). The author requests further explanation or a reference for this claim. However, there is no point in discussing nonlinear transformations in the first place, making it impossible for the speaker to provide any further insight.
  • #1
Kontilera
179
23
Hello! I'm currently reading Peskin and Schroeder and am curious about a qoute on page 38, which concerns representations of the Lorentz group.

”It can be shown that the most general nonlinear transformation laws can be built from these linear transformations, so there is no advantage in considering transformations more general than (3.8.).”

Where (3.8.) is,
[tex]\Phi_a(x) \rightarrow M_{ab}(\Lambda)\Phi_b(\Lambda^{-1}x).[/tex]

If anybody has time to expand this claim a bit I would be really happy, otherwise just give me a referens.

Thanks!
 
Physics news on Phys.org
  • #2
It's nonsense to discuss about nonlinear transformations in the first place, so I can't comment any further.
 
  • #3
Why is it nonsense? Would you like to explain?
 

1. What is the Lorentz group?

The Lorentz group is a mathematical concept that describes the transformations of space and time in special relativity. It is named after Dutch physicist Hendrik Lorentz and includes rotations and boosts in the four-dimensional Minkowski spacetime.

2. Why is the Lorentz group important?

The Lorentz group is important because it is the mathematical framework used to describe the laws of physics in special relativity. It is also essential in understanding the behavior of particles traveling at high speeds.

3. How is the Lorentz group represented?

The Lorentz group is typically represented by a matrix of 4x4 or 3x3 dimensions, depending on whether the transformations involve time or just space. These matrices are used to perform calculations and transformations in special relativity.

4. What are the implications of the Lorentz group?

The Lorentz group has several implications in physics, including the concept of time dilation and length contraction in special relativity. It also helps explain the constant speed of light and the equivalence of mass and energy in Einstein's famous equation, E=mc².

5. How is the Lorentz group related to the Standard Model of particle physics?

The Standard Model, which describes the fundamental particles and their interactions, is based on the principles of special relativity and therefore relies on the Lorentz group. The Lorentz transformations are used to describe the behavior of particles at high speeds, and the equations of the Standard Model are invariant under these transformations.

Similar threads

  • Differential Geometry
Replies
1
Views
1K
Replies
31
Views
3K
  • Special and General Relativity
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
936
Replies
15
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Special and General Relativity
Replies
6
Views
2K
Replies
13
Views
2K
  • Special and General Relativity
Replies
8
Views
5K
Back
Top