Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature?

This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology.

The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods.

Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

你是否曾經想過為什麼現代物理的語言圍繞著幾何學？或者量子算子和狄拉克括號是如何運作的？卷積究竟是什麼？張量又是什麼？場論和拉格朗日量是什麼，為什麼重力被描述為曲率？

本書將帶你探索構成現代數學物理語言的主要思想。在這裡，你將接觸到對於行列式和幾何學、波函數演化、統計學、信號處理以及三維旋轉等概念的新穎方法。你將看到特殊相對論的加速參考系如何告訴我們有關重力的資訊。在這段旅程中，你將發現張量符號如何與向量微積分相關，微分幾何如何建立在直觀概念之上，以及變分微積分如何導向場論。你將接觸到量子測量理論、格林函數和複數積分的藝術，最後還有廣義相對論和宇宙學。

本書對張量分析採取了一種全新的方法，僅基於度量和向量，無需使用一形式。這使得對於向量和張量微積分以及廣義相對論的幾何和直觀理解，比傳統的、更抽象的方法更為深入。

唐·科克斯（Don Koks）是澳大利亞阿德萊德國防科學與技術組織的物理學家。他的量子宇宙學博士學位來自阿德萊德大學的物理與數學物理系。之前在奧克蘭大學的工作專注於應用加速器物理，以及純粹和應用數學。

"With enjoyable and sometimes surprising excursions along the way, the journey provides a fresh look at many familiar topics, as it takes us from basic linear mathematics to general relativity... look forward to having your geometric intuition nourished and expanded by the author's intelligent commentaries."

Eugen Merzbacher, University of North Carolina, Chapel Hill

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature?

This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology.

The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods.

Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

「這段旅程伴隨著愉快且有時令人驚訝的探索，提供了對許多熟悉主題的新視角，從基本的線性數學到廣義相對論……期待透過作者的智慧評論來滋養和擴展你的幾何直覺。」

尤根·梅茲巴赫，北卡羅來納大學教堂山分校

你是否曾經想過為什麼現代物理的語言圍繞著幾何學？或者量子算子和狄拉克括號是如何運作的？卷積究竟是什麼？張量是什麼？或者場論和拉格朗日量是什麼，為什麼重力被描述為曲率？

這本書帶你探索構成現代數學物理語言的主要思想。在這裡，你將接觸到對於行列式和幾何學、波函數演化、統計學、信號處理以及三維旋轉等概念的新穎方法。你將看到特殊相對論的加速參考系如何告訴我們有關重力的資訊。在這段旅程中，你將發現張量符號如何與向量微積分相關，微分幾何如何建立在直觀概念之上，以及變分微積分如何導向場論。你將接觸到量子測量理論、格林函數和複數積分的藝術，最後是廣義相對論和宇宙學。

這本書對張量分析採取了一種全新的方法，僅基於度量和向量，無需一形式。這比傳統的、更抽象的方法提供了對向量和張量微積分以及廣義相對論更具幾何性和直觀的見解。

唐·科克斯是澳大利亞阿德萊德國防科學與技術組織的物理學家。他的量子宇宙學博士學位來自阿德萊德大學的物理與數學物理系。之前在奧克蘭大學的工作專注於應用加速器物理，以及純粹和應用數學。