We show that for a fermion in a bounded background potential in a finite box, eigenvalues of the total charge are independent of whether the potential is solitonic and depend only on the boundary condition: half-odd integral or integral for charge conjugation (C) invariant boundary conditions and an arbitrary fraction forC non-invariant boundary conditions. Fractional fermion numbers for infinite space Jackiw-Rebbi and Goldstone-Wilczek Hamiltonians are reproduced in finite space by using boundary conditions different from the periodic ones of Rajaraman and Bell.

We consider a fermion of chargee confined to a spherical bag with a Dirac monopole of strengthg at its centre. We find that the boundary conditions making the lowest angular momentum hamiltonian self-adjoint are characterized by a unitary matrixU, and the corresponding vacuum charge has a fractional part 2|eg|α/π where detU = -exp (2iα). Boundary conditions for conservation of helicity,CP, CT andPT are displayed. We demonstrate the possibility of a fractionally charged dyon whose interaction with a fermion conserves helicity. We also show thatthe simultaneous validity of helicity, CP, CT and PT requires integer vacuum charge.

We show that the classical Nambu-Goto string inD dimensions admits Poincaré invariance ind dimensions (d⩽D) if (i)d − 2 of the transverse co-ordinatesxⁱ are periodic and the rest quasi-periodic involving a real orthogonal matrix with (D − d) (D − d − 1)/2 free parameters, or if (ii)d − 2 ofxⁱ obey Neumann and the rest obey a boundary condition involvingN free parameters, whereN=(D − d)²/2 ifD − d is even, andN=[(D − d)² − 1]/2 ifD − d is odd.

Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than N+1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative definition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie-Bohm realistic theory gives highly nonclassical trajectories.