路径积分测度与微分同构不变性

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
Alfio Bonanno, Kevin Falls, Renata Ferrero
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引用次数: 0

摘要

就像作用一样,微分同胚不变性可以用来固定量子引力中路径积分测度的形式。此外,由于构成“行动”的要素与构成“措施”的要素之间存在冗余,因此人们总是可以选择后者的最小形式。然而,最近的论文[1,2]的作者已经提出了一种形式的量子引力路径积分测量,这是由Fradkin和Vilkovisky很久以前提出的,它不是不变的。这很容易看出,因为它显式地依赖于逆度规的g00分量,而不被压缩成标量。在[3]中提出了一个同样的非不变测度。正如他们的支持者所指出的,当使用这些措施时,通常出现的某些分歧是不存在的。然而,在所提出的措施中仍然存在的分歧,不出所料,既不是微分同构不变的,也不是监管的有效行动。我们通过计算自由标量场对引力有效作用发散部分的贡献,使用不同的度量和固有时间截止来明确地证明了这一点。我们通过对路径积分测量的深入讨论来支持我们的发现。特别是,我们看到如何从一个规范的设置中获得的贡献,可以用一种与微分同构不变性相容的关系方式重新解释。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Path integral measures and diffeomorphism invariance

Much like the action, diffeomorphism invariance can be used to fix the form of the path integral measure in quantum gravity. Moreover, since there is a redundancy between what constitutes “the action” and what constitutes “the measure” one can always pick a minimal form of the latter. However, the authors of recent papers [1, 2] have advocated a form of the path integral measure for quantum gravity, proposed long ago by Fradkin and Vilkovisky, that is not invariant. This is easily seen since it depends explicitly on the g00 component of the inverse metric without being contracted to form a scalar. An equally non-invariant measure was proposed in [3]. As noted by their proponents, when these measures are used, certain divergences that typically appear are absent. However, the divergences that remain with the proposed measures are, unsurprisingly, neither diffeomorphism-invariant nor is the regulated effective action. We demonstrate this explicitly by computing the free scalar field contribution to the divergent part of the gravitational effective action using different measures and a proper-time cutoff. We support our findings with a thorough discussion of the path integral measure. In particular, we see how the contributions from the measure, obtained in a canonical setting, could be reinterpreted in a relational way compatible with diffeomorphism invariance.

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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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