Classical Euclidean Wormhole Solution and Wave Function for a Nonlinear Scalar Field

摘要

In this paper we consider the classical Euclidean wormhole solution of the Born—Infeld scalar field. The corresponding classical Euclidean wormhole solution can be obtained analytically for both very small and large $dot varphi$ . At the extreme limit of small $dot varphi$ the wormhole solution has the same format as one obtained by Giddings and Strominger (Nuclear Physics B 306, 890, 1988). At the extreme limit of large $dot varphi$ the wormhole solution is a new one. The wormhole wave functions can also be obtained for both very small and large $dot varphi$ . These wormhole wave functions are regarded as solutions of quantum-mechanical Wheeler—Dewitt equation with certain boundary conditions.