Question

Indicate how the following quantities will transform under the P (space inversion) and T (time reversal) operation: 

(a) Position coordinate r 

(b) Momentum vector P 

(c) Spin or angular momentum vector σ = r × P 

(d) Electric field E = −∇V 

(e) Magnetic field B = i × r 

(f) Electric dipole moment σ.E 

(g) Magnetic dipole moment σ.B

Answer 1

(a) r → −r under P- operation as x → −x, y → −y and z → −z but r → r under T- operation. 

(b) P reverses its sign under both P and T operation, P → −P. Both r and p are known as polar vectors. 

(c) σ or L are axial vectors. σ = r × p. Since both r and p change their sign under P-operation, L does not. However under T-operation r does not change sign but p does and so σ changes its sign. 

(d) E = −∂V/∂r for the above argument changes sign under P-operation as r changes its sign and does not under T-operation as r does not. 

(e) The magnetic field like angular momentum is an axial vector B = i × r. Under p-operation B → B because i → −i and r → −r but under T-operation because r → r and i → −i so that B → −B

(f) σ.E → −σ.E under both P and T-operations. 

(g) Similarly σ.B → −σ.B under both p-operation and under T-operation.