Relation between symmetry, charges and one-particle states

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SUMMARY

The discussion centers on the relationship between symmetry, charges, and one-particle states in quantum mechanics. It highlights the assertion that if a symmetry leaves one-particle states invariant, then the associated charge operator Q acts on these states such that Q|p> = 0. This principle is crucial for understanding how symmetries influence particle states and their corresponding charges.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of symmetry operations in physics
  • Familiarity with one-particle state notation
  • Basic knowledge of charge operators in quantum field theory
NEXT STEPS
  • Study the implications of Noether's theorem in quantum mechanics
  • Research the role of symmetry in quantum field theory
  • Explore the mathematical formulation of charge operators
  • Investigate examples of invariance in one-particle states
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in the interplay between symmetry and particle physics.

alphaone
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Hi,
I recently saw an author make the following statement:
If the symmetry leaves the 1-particle states invariant then its associated charge Q acts on the 1-particle states |p> such that Q|p> = 0
This statement is nontrivial to me, so if anybody could show me how it works please let me know.
 
Physics news on Phys.org
Figured this out myself already, so no reply needed.
 

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