When a massless, isospinor Dirac field is confined to a finite region of space by means of a chiral boundary condition parametrized by an angle $\theta$, the baryon number of the vacuum is shown to be $\left(\frac{\chi }{2\pi }\right)(\theta -sin\theta cos\theta )$ where $\chi$ is the Euler characteristic of the bounding surface. Some implications for chiral bag models are discussed.

• Received 15 August 1983

DOI:https://doi.org/10.1103/PhysRevLett.51.1518