We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous \((2+1)\)-dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge B-field, and central charge deficit term \(\varLambda \). At the quantum level, solutions of Wheeler–DeWitt equations have been enriched by considering the quantum versions of the classical conditional symmetry equations. Concerning the possible applications of the obtained solutions, the semiclassical analysis of Bohm’s mechanics has been performed to demonstrate the possibility of avoiding the classical singularities at the quantum level.

我们介绍了三类经典和量子解，它们针对的是空间均质\（（2 + 1）\）-维时空上的弦有效作用的先导顺序，其来源来自dilaton，反对称规范B场，和中央电荷赤字项\（\ varLambda \）。在量子水平上，通过考虑经典条件对称方程的量子形式，丰富了Wheeler-DeWitt方程的解。关于获得的解决方案的可能应用，已对Bohm力学进行了半经典分析，以证明在量子水平上避免经典奇异性的可能性。