Foundational Issues in Group Field Theory

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2024-05-20 DOI:10.1007/s10701-024-00763-9

Álvaro Mozota Frauca

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Abstract

In this paper I offer an introduction to group field theory (GFT) and to some of the issues affecting the foundations of this approach to quantum gravity. I first introduce covariant GFT as the theory that one obtains by interpreting the amplitudes of certain spin foam models as Feynman amplitudes in a perturbative expansion. However, I argue that it is unclear that this definition of GFTs amounts to something beyond a computational rule for finding these transition amplitudes and that GFT doesn’t seem able to offer any new insight into the foundations of quantum gravity. Then, I move to another formulation of GFT which I call canonical GFT and which uses the standard structures of quantum mechanics. This formulation is of extended use in cosmological applications of GFT, but I argue that it is only heuristically connected with the covariant version and spin foam models. Moreover, I argue that this approach is affected by a version of the problem of time which raises worries about its viability. Therefore, I conclude that there are serious concerns about the justification and interpretation of GFT in either version of it.

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群体场论的基础问题

在本文中，我将介绍群场论（GFT）以及影响这种量子引力方法基础的一些问题。我首先介绍了协变 GFT，即把某些自旋泡沫模型的振幅解释为微扰展开中的费曼振幅而得到的理论。然而，我认为，除了找到这些跃迁振幅的计算规则之外，GFT 的这一定义是否还等同于其他东西并不清楚，而且 GFT 似乎并不能为量子引力的基础提供任何新的见解。然后，我转到 GFT 的另一种表述，我称之为规范 GFT，它使用量子力学的标准结构。这种表述在 GFT 的宇宙学应用中有着广泛的用途，但我认为它只是启发式地与协变版本和自旋泡沫模型相联系。此外，我还认为这种方法受到时间问题版本的影响，使人担心其可行性。因此，我的结论是，无论哪个版本的GFT，其合理性和解释都令人严重担忧。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.