论文标题
E10 Wheeler-Dewitt操作员低级别
The E10 Wheeler-DeWitt operator at low levels
论文作者
论文摘要
我们考虑了与Hamiltonian的Bosonic部分D = 11超级重力相关联的Wheeler-Dewitt操作员，仅具有三型和六型领域的空间组件，并将其与E10 Casimir操作员的空间组件与低水平进行比较，以表明这两个操作员与这两个操作员完全匹配了Modulo Pastial渐变级别，并包括两个级别（包括GL（10））。 E10 Casimir操作员的独特性消除了量子哈密顿量中的所有秩序歧义，至少达到所考虑的水平。除了第三级以外，这两个操作员将开始彼此不同，因为他们为经典表达式提供了差异。 We then consider truncations of the E10 Wheeler-DeWitt operator for various finite-dimensional subgroups of E10 in order to exhibit the automorphic properties of the associated wave functions and to show that physically sensible wave functions generically vanish at the cosmological singularity, thus providing new and more sophisticated examples of DeWitt's proposed mechanism for singularity resolution in quantum gravity.我们的构造提供了有关Wheeler-Dewitt方程的几个未解决的概念问题的新观点，例如量子重力中观察物的问题，或在纯粹的代数框架中出现的新兴空间和时间问题。我们还重点介绍了E10框架的剩余问题。
We consider the Wheeler-DeWitt operator associated with the bosonic part of the Hamiltonian of D=11 supergravity in a formulation with only the spatial components of the three-form and six-form fields, and compare it with the E10 Casimir operator at low levels, to show that these two operators precisely match modulo spatial gradients up to and including gl(10) level two. The uniqueness of the E10 Casimir operator eliminates all ordering ambiguities in the quantum Hamiltonian, at least up to the level considered. Beyond level three the two operators are expected to start to differ from each other, as they do so for the classical expressions. We then consider truncations of the E10 Wheeler-DeWitt operator for various finite-dimensional subgroups of E10 in order to exhibit the automorphic properties of the associated wave functions and to show that physically sensible wave functions generically vanish at the cosmological singularity, thus providing new and more sophisticated examples of DeWitt's proposed mechanism for singularity resolution in quantum gravity. Our construction provides novel perspectives on several unresolved conceptual issues with the Wheeler-DeWitt equation, such as the question of observables in quantum gravity, or the issue of emergent space and time in a purely algebraic framework. We also highlight remaining open questions of the E10 framework.
