Search for C-violating, P-conserving interactions and observation of 2{sup 3}S{sub 1} to 2{sup 1}P{sub 1} transitions in positronium

CP-invariance forbids single photon transitions between w{sup 3}S{sub 1} states of positronium. Experimental limits are placed on the CP-violating state-mixing matrix element: {vert_bar} {r_angle}2{sup 1}P{sub 1}{vert_bar}H{sub P}{vert_bar}2{sup 3}P{sub 1}{r_angle}{vert_bar}<65MHz which are 3.6% of the 1,826 MHz 2{sup 1}P{sub 1}, 2{sup 3}P{sub 1} splitting. Comparable values for the neutral kaons are: {vert_bar}{l_angle}K{sub 1}{vert_bar}H{sub P}{vert_bar}K{sub 2}{r_angle} {vert_bar} = 2.7MHz and {vert_bar}{Delta}m-i{Delta}{Gamma}/2{vert_bar}=1230MHz. Applying a static magnetic field the 2{sup 3}S{sub 1} to 2{sup 1}P{sub 1} transition becomes allowed, which yields: (1) the calibration of the CP experiment, (2) the first observation of the 2{sup 1}P{sub 1} state, and (3) the first measurement of the 2{sup 3}S{sub 1} to 2{sup 1}P{sub 1} transition frequency, {nu}{sub o} = (11181 {plus_minus} 13)MHz, in agreement with QED calculations.