Geometry at the Quantum Scale: Understanding the Geometric Language of Relativistic Quantum Mechanics
暫譯: 量子尺度的幾何：理解相對論量子力學的幾何語言
Maia, Marcos D., Monte, Edmundo M.
- 出版商: Springer
- 出版日期: 2025-08-21
- 售價: $4,520
- 貴賓價: 9.5 折 $4,294
- 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)
這本書提出了一種單一的幾何語言，用於描述從二十世紀初至今所發現的基本物理學。前兩章簡要總結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）以及引力。這些章節還總結了高能物理學的主要實驗結果，包括在大型強子對撞機（LHC）發現的希格斯粒子存在的意義，以及最近天文觀測的意義。隨後的章節包括基於't Hooft-Veltman重整化定理對規範場的影響以及愛因斯坦廣義相對論的引力場的非重整化的量子引力。
本書的主要重點在於顯示三種規範力是在量子領域中定義的，而愛因斯坦的引力則仍然是一種本質上經典的相互作用。然而，愛因斯坦推理的主要意義體現在愛因斯坦-希爾伯特作用原則中，該原則與引力的來源無關。因此，愛因斯坦-希爾伯特原則本身不依賴於任何特定的來源，導致一個比廣義相對論所定義的引力場更為一般的引力場，同時保留了所有幾何特徵。這在意義上造成了關鍵的差異，因為現在所有四種基本相互作用都可以在同一量子領域中定義。愛因斯坦的廣義相對論的經典理論成為由愛因斯坦-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，這四種幾何的直接和產生了一種11維的黎曼幾何，其曲率定義了一種新的量子宇宙學，沒有層級結構，因此所有基本相互作用有效地貢獻於宇宙的演化，這一結果對高能物理學家、宇宙學家、數學家、哲學家以及所有尋求對物理世界合理解釋的人來說都具有興趣。
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)
馬爾科斯·杜阿特·邁亞出生於巴西北里約格朗德州。他在巴西戈亞斯州立大學學習工程，並於1966年在巴西利亞大學獲得物理學學士學位，指導教授為傑梅·蒂奧莫。1967年，他移居倫敦，作為倫敦大學國王學院的研究生與赫爾曼·邦迪合作研究引力波。不久之後，邦迪轉到維也納的ESRO計劃，他的指導轉交給克萊夫·基爾米斯特教授。1971年，他就愛丁頓的基本理論辯護了論文。返回巴西後，他於1971年被巴西利亞大學數學系聘用，並在那裡工作了20年，之後轉到同一大學的物理學研究所。1975年，他在劍橋大學的DAMTP擔任高級訪客，參與霍金的迷你黑洞研究小組。1982年至1984年間，他是意大利的國際理論物理中心（ICTP）的副會員訪客，參與卡魯扎-克萊因統一計劃。1985年，他在西雅圖的華盛頓大學擔任訪問科學家。在西雅圖的計劃結束後，他轉到加州聖巴巴拉的理論物理研究所，並作為研究訪客前往斯坦福線性加速器（SLAC）。1993年，他在芝加哥附近的NASA-費米實驗室天體物理中心擔任訪問科學家。他目前的職位是巴西利亞大學物理學研究所的退休高級研究員。
埃德蒙多·馬里尼奧·杜·蒙特擁有巴西巴拉伊巴聯邦大學（UFPB）的數學學士學位、UFPB的氣象科學碩士學位，以及巴西利亞大學（UnB）的數學博士學位，論文主題為廣義相對論。他曾在西班牙格拉納達大學的幾何與拓撲系擔任相對論的博士後研究員，並在意大利的國際理論物理中心（ICTP）和西班牙的UGR擔任訪問教授。他通過競爭進入UFPB，成為數學系的教授。目前，他是巴西巴拉伊巴聯邦大學（UFPB）物理系的正教授，位於巴西若昂佩索阿。他在物理和數學領域擁有經驗，重點研究時空浸入中的基本幾何問題，主要工作主題包括：偽黎曼流形的浸入、時空浸入、時空的幾何與拓撲、特殊與廣義相對論、宇宙學和引力。
