The classical wormhole solution and wormhole wavefunction with a nonlinear Born-Infeld scalar field

On this paper we consider the classical wormhole solution of the Born-Infeld scalar field. The corresponding classical wormhole solution can be obtained analytically for both very small and large $\dot{\varphi }$. At the extreme limits of small $\dot{\varphi }$ the wormhole solution has the same format as one obtained by Giddings and Strominger[10]. At the extreme limits of large $\dot{\varphi }$ the wormhole solution is a new one. The wormhole wavefunctions can also be obtained for both very small and large $\dot{\varphi }$. These wormhole wavefunctions are regarded as solutions of quantum-mechanical Wheeler–Dewitt equation with certain boundary conditions.