Spinor Boosts: Weinberg's QFT Book Insights on Rotation and Momentum Effects

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SUMMARY

Weinberg's Quantum Field Theory (QFT) book establishes that the effect of rotation on a massive particle's spin can be represented as exp(-i θ J.n), simplifying calculations significantly. However, the discussion highlights challenges in applying similar principles to boosts, particularly regarding massless particles. Participants express difficulty in deriving the Wigner rotation for boosts, as outlined in Weinberg's Volume I, Chapter 2. The need for a general theorem analogous to that for rotations is emphasized, indicating a gap in accessible methodologies for boost calculations.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT)
  • Familiarity with spinor representations
  • Knowledge of Wigner rotations
  • Concept of little group elements in particle physics
NEXT STEPS
  • Research the application of little group elements for boosts in QFT
  • Study Wigner rotation derivations in detail
  • Explore advanced topics in massless particle behavior in QFT
  • Examine alternative methods for simplifying boost calculations
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Physicists, particularly those specializing in Quantum Field Theory, theoretical physicists working on particle dynamics, and students seeking to deepen their understanding of spin and boost transformations.

mahdiarnt@yahoo.com
Weinberg shows in his book on QFT that the effect of a rotation on a
massive particle's spin is the same as applying exp(-i \theta J.n) on
the state, regardless of particle's momentum. In other words just
rotate the spinor in its own representation. This makes calculations
very simple. But what about boosts? There is of course a general
approach described in Weinberg's book using little group elements; but
it is too difficult to apply it each time. Is there any general theorem
for boost like that Weinberg presented for rotations? And also what
about massless particles?
 
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I´m finding the exact same problem. In fact I´m trying to solve the first problem in Weinberg Vol I. Chpater 2 and while all the other items I managed to find out, I still hhave many problems in getting the Wigner rotation for the Boost.
 

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