Classify each of the following quantities as a scalar

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

Classify each of the following quantities as a scalar, pseudoscalar, vector or axial vector under the parity operator P^\hat P, and justify each answer from the transformation of x\mathbf{x}, p\mathbf{p} and spin S\mathbf{S} (which behaves under P^\hat P like an orbital angular momentum r×p\mathbf{r}\times\mathbf{p}). ((a)) A magnetic field B\mathbf{B}. ((b)) The electric dipole moment d=∑iqixi\mathbf{d}=\sum_i q_i\mathbf{x}_i of a distribution of charges qiq_i at positions xi\mathbf{x}_i. ((c)) The helicity h=S⋅p^h = \mathbf{S}\cdot\hat{\mathbf{p}}, where p^=p/∣p∣\hat{\mathbf{p}}=\mathbf{p}/|\mathbf{p}|. ((d)) The kinetic energy T=p2/2mT = p^2/2m.

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