Missing Momentum Research Articles

Experiments on the Emission of Neutrinos fromP32

These experiments study energy and momentum conservation in beta-decay. The apparatus, improved over earlier experiments, permits increased accuracy in the measurement of the neutrino-electron angular correlation. It is concluded that the correlation is approximately ($1+cos\ensuremath{\theta}$). Determination of the nature of the dominant interaction in the beta-decay of ${\mathrm{P}}^{32}$ awaits measurement of the nuclear spin. If the spin is one, the tensor interaction is uniquely selected. If the spin is zero, the axial vector dominates. Spin 2 or higher is ruled out by the shape of the beta-spectrum.It is also demonstrated that in beta-decay the missing energy and the missing momentum obey the relation $p=\frac{E}{c}$ to an accuracy of better than 10 percent.

A note on the Hamiltonian theory of quantization. II

It is pointed out that the equations of motion for any field obtained by varying a Lagrangian subject to auxiliary conditions are exactly equivalent to a certain set of canonical equations and that the commutation relations between the dynamical variables for the latter equations are Lorentz-invariant. By extending the theory to Lagrangians containing higher derivatives of the field quantities, it is shown that any given set of field equations can be put into the canonical form, though it is not derived from variational principles. The question of Lagrangians with missing momenta is also considered. It is shown that if the Lagrangian is ‘gauge-invariant’, some of the p's must be missing and the corresponding Eulerian equations can be replaced by equations containing no q and then can be replaced by initial conditions. The commutation relations between gauge-invariant quantities are Lorentz-invariant. For Lagrangians which are not gauge-invariant but are such as to have missing momenta, the passage to quantum theory will in general give rise to non-Lorentz-invariant commutation relations. In both cases, the equations of motion can be cast in canonical forms.