We review work on constrained systems in which (3+1)-dimensional field theories are reduced to effective (2+1)-dimensional ones. Known results are extended to encompass the Dirac equation and the nonrelativistic limit is examined. We discuss to what extent this system can really be made two dimensional and obtain a lower bound on the thickness. Some comments are made about recent theories involving fractional statistics.PACS number(s): 03.65. -w

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Erratum: Quantum mechanics of a constrained electrically charged particle in the presence of electric currents [Phys. Rev. A 80, 052109 (2009)]

We show that a two dimensional wormhole geometry is equivalent to a catenoid, a minimal surface. We then obtain the curvature induced geometric potential and show that the ground state with zero energy corresponds to a reflectionless potential. By introducing an appropriate coordinate system we also obtain bound states for different angular momentum channels. Our findings can be realized in suitably bent bilayer graphene sheets with a neck or in a honeycomb lattice with an array of dislocations or in nanoscale waveguides in the shape of a catenoid.

In this article we study the properties of certain quantum systems outside a rotating cosmic gauge string. It is shown that particle energies couple to the angular momentum density in the string, even though the particles are constrained only to move outside the string core where the Riemannian curvature vanishes identically. This effect may be looked upon as a gravitational analog of the Aharanov–Bohm effect. Due to the coupling of the particle energy to the angular momentum density in the string, it is shown that the angular momentum spectrum of the quantum particle is shifted by a constant amount. This, it is argued, will give rise to an nonvanishing angular momentum density in the quantum vacuum outside the rotating string. It is also shown that a quantum particle might experience an infinite blueshift in the presence of closed timelike curves outside such a string.