Twisted scalar and spinor strings in Minkowski spacetime

Abstract

The construction of twisted scalar and spinor field configurations in Minkowski spacetime is described. Twisted field configurations are normally associated with a nonsimply connected space; however, it is shown that it is also possible to construct such configurations in a simply connected space. For each choice of a line in three-dimensional space there exists an inequivalent twisted scalar and spinor field configuration, referred to as strings. The vacuum expectation value of the energy-momentum tensor of such a quantized twisted field is calculated for the case of both scalar strings and spinor strings. It is found to be singular along the chosen line. The energy density off of this line is positive for scalar strings and negative for spinor strings. However, it is shown that the total energy of both types of strings is zero. Nonrelativistic quantum mechanics of these twisted field configurations is discussed, and the eigenfunctions and energy levels of a twisted particle in a Coulomb field are calculated.