Regarding representations of the Lorentz group

Click For Summary
SUMMARY

The discussion centers on the representations of the Lorentz group as presented in Peskin and Schroeder's text. Specifically, it addresses the quote regarding the irrelevance of nonlinear transformations in the context of linear transformations, as stated in equation (3.8). Participants express skepticism about the utility of nonlinear transformations, emphasizing that the linear transformations sufficiently describe the behavior of fields under Lorentz transformations. The consensus suggests a focus on linear representations for clarity and effectiveness in theoretical physics.

PREREQUISITES
  • Understanding of Lorentz transformations
  • Familiarity with quantum field theory concepts
  • Knowledge of Peskin and Schroeder's "An Introduction to Quantum Field Theory"
  • Basic grasp of mathematical representations in physics
NEXT STEPS
  • Study the implications of linear transformations in quantum field theory
  • Research the mathematical structure of the Lorentz group
  • Examine the role of nonlinear transformations in theoretical physics
  • Explore advanced topics in representation theory related to particle physics
USEFUL FOR

The discussion is beneficial for theoretical physicists, graduate students in quantum field theory, and anyone interested in the mathematical foundations of particle physics, particularly those studying the Lorentz group and its representations.

Kontilera
Messages
176
Reaction score
24
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,
\Phi_a(x) \rightarrow M_{ab}(\Lambda)\Phi_b(\Lambda^{-1}x).

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
It's nonsense to discuss about nonlinear transformations in the first place, so I can't comment any further.
 
Why is it nonsense? Would you like to explain?
 

Similar threads

Graduate In what representation do Dirac adjoint spinors lie?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Discussing the mathematical formalism of generators (Lorentz Group)
  • · Replies 31 ·
2
Replies
31
Views
5K
Undergrad 6-dimensional representation of Lorentz group
  • · Replies 6 ·
Replies
6
Views
2K
Lorentz algebra elements in an operator representation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate QFT: Lorentz Trans+ Field infinitesimal variation
  • · Replies 15 ·
Replies
15
Views
3K
General Irreducible Representation of Lorentz Group
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Representation of Lorentz group and spinors (in Peskin page 38)
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Spinor Representation of Lorentz Transformations: Solving the Puzzle
  • · Replies 6 ·
Replies
6
Views
3K
Lie groups,Lie algebras, Physics, Lorentz Group,
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Proof than an equation is Lorentz invariant
  • · Replies 8 ·
Replies
8
Views
6K