Geometry at the Quantum Scale: Understanding the Geometric Language of Relativistic Quantum Mechanics
Maia, Marcos D., Monte, Edmundo M.
- 出版商: Springer
- 出版日期: 2025-02-17
- 售價: $5,020
- 貴賓價: 9.5 折 $4,769
- 語言: 英文
- 頁數: 160
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031611969
- ISBN-13: 9783031611964
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相關分類:
量子 Quantum
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商品描述
This book presents a single geometric language for the fundamental physics that has been discovered from the beginning of the twentieth century to the present day. The first two chapters give a brief summary of the four known fundamental forces, namely the three known gauge forces (the electromagnetic and the two nuclear forces) and the gravitational force. These chapters also summarize the main experimental results from high energy physics, including the implications of the existence of the Higgs particle discovered at the LHC, and the implications of recent astronomical observations. The subsequent chapters include quantum gravity based on the consequences of the't Hooft-Veltman renormalization theorem for gauge fields and the non-renormalization of Einstein's gravitational field of General Relativity.
The main focus of the book is to show that the three gauge forces are defined in the quantum domain, while Einstein's gravitation remains an essentially classical interaction. However, the main implication of Einstein's reasoning is built into the Einstein-Hilbert action principle, which is independent of the source of gravitation. As such, the Einstein-Hilbert principle by itself does not depend on any specific source, leading to a gravitational field that is far more general than that defined by General Relativity, while retaining all its geometrical characteristics. This makes a key difference in the sense that all four fundamental interactions may now be defined in the same quantum domain. Einstein's classical theory of General Relativity becomes a particular case of the quantum gravitational field defined by the Einstein-Hilbert action.
At the quantum scale, the direct sum of the resulting four geometries produces an 11-dimensional Riemannian geometry whose curvature defines a new quantum cosmology without hierarchies, so that all fundamental interactions contribute effectively to the evolution of the universe, a result that is of interest to high energy physicists, cosmologists, mathematicians, philosophers and all those who seek a plausible explanation for the physical world.
商品描述(中文翻譯)
本書提出了一種統一的幾何語言，用於描述從20世紀初至今所發現的基礎物理學。前兩章簡要介紹了四種已知的基本力，即三種已知的規範力（電磁力和兩種核力）和引力。這些章節還總結了高能物理學的主要實驗結果，包括在LHC發現的希格斯粒子的存在以及最近天文觀測的影響。接下來的章節包括基於't Hooft-Veltman規範場的重整化定理和愛因斯坦廣義相對論引力場的不可重整性的量子引力。
本書的主要重點是顯示三種規範力在量子領域中被定義，而愛因斯坦的引力則仍然是一種基本的古典相互作用。然而，愛因斯坦的推理的主要含義被建立在愛因斯坦-希爾伯特作用原理中，該原理與引力的來源無關。因此，愛因斯坦-希爾伯特原理本身不依賴於任何特定的源頭，從而產生了一個比廣義相對論定義的引力場更為普遍的引力場，同時保留了所有的幾何特徵。這在一個關鍵的意義上有所不同，因為現在可以在同一個量子領域中定義所有四種基本相互作用。愛因斯坦的古典廣義相對論理論成為了由愛因斯坦-希爾伯特作用定義的量子引力場的一個特例。
在量子尺度上，這四種幾何的直和產生了一個11維黎曼幾何，其曲率定義了一個沒有層次結構的新量子宇宙學，以便所有的基本相互作用有效地貢獻於宇宙的演化，這對於高能物理學家、宇宙學家、數學家、哲學家以及所有尋求對物理世界提供合理解釋的人都是一個有趣的結果。
作者簡介
Marcos Duarte Maia was born in the state of North Rio Grande, Brazil. He studied engineering at the State University of Goiás (Brazil), and obtained a BSc degree in Physics in 1966 at the University of Brasilia under supervision of Jayme Tiomno. He moved to London in 1967 to work with Hermann Bondi on gravitational waves as a research student at King's College of the University of London. Soon after, Bondi moved to the ESRO program in Vienna, and his supervision was transferred to Professor Clive Kilmister. In 1971 he defended a thesis on the subject of Eddington's Fundamental Theory. After his return to Brazil, he was hired by the Department of Mathematics of the University of Brasilia in 1971, where he stayed for the next 20 years, before moving to the Physics Institute of the same university. In 1975, he was a Senior Visitor at the DAMTP, University of Cambridge, in Hawking's group on mini black holes. In the period of 1982 to 1984, he was a an Associate Member visitor to the ICTP (Trieste, Italy) working on the Kaluza-Klein unification program. In 1985 he was a visiting scientist at the University of Washington at Seattle. At the end of his program in Seattle, he moved to the Institute of Theoretical Physics at Santa Barbara, California, and as a research visitor to the Stanford Linear Accelerator (SLAC). In 1993, he was a Visiting Scientist at the NASA-Fermilab Astrophysical Center near Chicago. His present position is as a Retired Senior Research Associate at the Institute of Physics of the University of Brasilia.
Edmundo Marinho do Monte has a bachelor's degree in mathematics from the Federal University of Paraíba (UFPB), Brazil, a master's degree in atmospheric sciences from UFPB, Brazil, and a PhD in mathematics from the University of Brasília (UnB), Brazil, with a thesis in general relativity. He was a Postdoctoral researcher in relativity at the Department of Geometry and Topology, Granada University (UGR, Spain) and has held visiting professor positions at the International Center for Theoretical Physics (ICTP), Italy, and UGR, Spain. He entered UFPB through competition as a Professor in the Department of Mathematics at UFPB. He is currently Full Professor at the Department of Physics at UFPB, João Pessoa, Brazil. He has experience in the area of physics and mathematics, with an emphasis on fundamental geometric problems in spacetime immersions, working mainly on the following topics: immersions of pseudo-Riemannian manifolds, space-time immersions, geometry and topology of space-times, special and general relativity, cosmology and gravitation.
作者簡介(中文翻譯)
Marcos Duarte Maia出生在巴西北里奧格蘭德州。他在巴西戈亞斯州立大學學習工程學，並於1966年在巴西利亞大學獲得物理學學士學位，由Jayme Tiomno指導。他於1967年移居倫敦，在倫敦大學國王學院擔任研究生，與Hermann Bondi合作研究引力波。不久之後，Bondi轉到維也納的ESRO計劃，他的指導轉交給Clive Kilmister教授。1971年，他以愛丁頓的基本理論為題進行了論文辯護。回到巴西後，他於1971年被巴西利亞大學數學系聘用，並在接下來的20年內留在該大學，然後轉到該大學的物理學院。1975年，他在劍橋大學DAMTP擔任高級訪問學者，加入霍金的小黑洞研究小組。1982年至1984年期間，他在國際理論物理中心（ICTP，意大利的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的的
