论文标题
量化Eisenhart升降机
Quantizing the Eisenhart Lift
论文作者
论文摘要
经典的Eisenhart升力是一种方法，可以通过这种方法通过在高维弯曲的歧管（称为举起的歧管）中演变的自由系统来重新创建具有电势的经典系统的动力学。我们将Eisenhart Lift的配方扩展到量子系统，并表明抬高的歧管不仅重现了电势的经典效应，还重现了其量子机械效应。特别是，我们发现，在投射新的自由度之后，提起系统的Schrodinger方程的解决方案减少了原始系统的解决方案。在这种情况下，我们确定了一个保守的量子数，这与经典系统的提升动量相对应。我们进一步将Eisenhart升力应用于量子场理论（QFT）。我们表明，提起的场空间歧管能够重现标量场电位的经典和量子效应。我们发现，在QFT的情况下，提升动量的类似物是一种量子电荷，不仅可以及时而且在太空中也是保守的。该电荷标签的不同可能值一个彼此之间都不相交的Fock空间的集合。这些扩展的Fock空间与宇宙常数和仪表层次结构问题的相关性。
The classical Eisenhart lift is a method by which the dynamics of a classical system subject to a potential can be recreated by means of a free system evolving in a higher-dimensional curved manifold, known as the lifted manifold. We extend the formulation of the Eisenhart lift to quantum systems, and show that the lifted manifold recreates not only the classical effects of the potential, but also its quantum mechanical effects. In particular, we find that the solutions of the Schrodinger equations of the lifted system reduce to those of the original system after projecting out the new degrees of freedom. In this context, we identify a conserved quantum number, which corresponds to the lifted momentum of the classical system. We further apply the Eisenhart lift to Quantum Field Theory (QFT). We show that a lifted field space manifold is able to recreate both the classical and quantum effects of a scalar field potential. We find that, in the case of QFT, the analogue of the lifted momentum is a quantum charge that is conserved not only in time, but also in space. The different possible values for this charge label an ensemble of Fock spaces that are all disjoint from one another. The relevance of these extended Fock spaces to the cosmological constant and gauge hierarchy problems is considered.
