A spin- particle with spin operator is searched for a permanent electric dipole…
PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model
Symmetry and Flavour, Ch Parity, charge conjugation and time reversal as operators, and the CPT theorem
Problem
A spin-21 particle with spin operator S=2ℏσ is searched for a permanent electric dipole moment through the interaction energy HEDM=−dσ⋅E, where d is a constant characteristic of the particle (its electric dipole moment) and E is an external electric field.
((a)) State how σ (an angular momentum) and E (a polar vector, the field of static charges) each transform under the parity operator P^ and under the time-reversal operator T^.
((b)) Use these transformations to show that HEDM changes sign under P^ and changes sign under T^, taken separately.
((c)) Explain why a nonzero measured d for an elementary spin-21 particle in a non-degenerate ground state shows that both P and T are violated by whatever interaction produces d, given that the particle's spin is the only vector available to build the operator.