We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to full Quantum Gravity. We advocate the point of view that quantum field theories should be regularized by sequences of quasi-physical systems comprising a well defined number of the field's degrees of freedom. In dependence on this number, each system backreacts autonomously and self-consistently on the gravitational field. In this approach, the limit which removes the regularization automatically generates the physically correct spacetime geometry, i.e., the metric the quantum states of the field prefer to "live" in. We apply the scheme to a Gaussian scalar field on maximally symmetric spacetimes, thereby confronting it with the standard approaches. As an application, the results are used to elucidate the cosmological constant problem allegedly arising from the vacuum fluctuations of quantum matter fields. An explicit calculation shows that the problem disappears if the pertinent continuum limit is performed in the improved way advocated here. A further application concerns the thermodynamics of de Sitter space where the approach offers a natural interpretation of the micro-states that are counted by the Bekenstein-Hawking entropy.

中文翻译：

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具有重力耦合逼近序列的背景独立场量化

我们概述、测试并应用了一种新方案，用于对与动态重力接触的量化场系统进行非微扰分析。虽然本文对引力进行了经典处理，但该方法本身适用于全量子引力的泛化。我们主张这样一种观点，即量子场论应该通过准物理系统序列进行正则化，这些系统包括明确定义的场自由度数。根据这个数字，每个系统都会在引力场上自主和自洽地进行反向反应。在这种方法中，消除正则化的限制会自动生成物理上正确的时空几何，即场的量子态更喜欢“存在”的度量。我们将该方案应用于最大对称时空中的高斯标量场，从而用标准方法对付它。作为应用，该结果用于阐明据称由量子物质场的真空涨落引起的宇宙常数问题。一个明确的计算表明，如果相关的连续体限制以这里提倡的改进方式执行，问题就会消失。另一个应用涉及德西特空间的热力学，其中该方法提供了对 Bekenstein-Hawking 熵计数的微观状态的自然解释。一个明确的计算表明，如果相关的连续统限制以这里提倡的改进方式执行，问题就会消失。另一个应用涉及德西特空间的热力学，其中该方法提供了对 Bekenstein-Hawking 熵计数的微观状态的自然解释。一个明确的计算表明，如果相关的连续体限制以这里提倡的改进方式执行，问题就会消失。另一个应用涉及德西特空间的热力学，其中该方法提供了对 Bekenstein-Hawking 熵计数的微观状态的自然解释。