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如何成为一名优秀的理论物理学家
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如何成为一名优秀的理论物理学家
作者：Gerard 't Hooft
　　本文作者Gerard 't Hooft，荷兰人，1999年诺贝尔物理学奖得主，当今理论物理学的大牛。如果对物理学感兴趣而不知道Gerard 't Hooft，那么我的建议是，要么自己去查找资料，要么乘早去关心其他任何除了物理学之外的东西。
　　本文有不同的译本，全部都让人感觉作者是那个智商才75的小扑屎，而不是一个堂堂诺贝尔物理学奖得主，我一个也不满意。于是，自己动手，丰衣足食。
　　这个网站（在建中）为青年学生和其他任何人所做——那些和我一样面对真正科学的挑战而兴奋的人，那些和我一样决定以他们的大脑在我们生活的现实世界中做出新发现的人。简而言之，是为了那些决定以毕生精力研究理论物理学的人。
　　我经常收到来自业余物理学家们的计划周密而一无是处的信件，他们坚信自己已经解释了整个世界。他们坚信这一点，只是因为他们对于解决现代物理学问题的真正方法完全一窍不通。如果你真的想对物理学定律的理论解释作出贡献——如果你成功了，那将是一种令人兴奋的体验！——你需要懂的东西太多了。首先，要认真对待之。所有必要的科学课程都是在大学中教的，因此，很自然，你首先要做的事就是读大学并学习你能够学到的所有知识。但是，如果你还年轻，还在上中学，你进大学之前不得不忍受那些被称之为幼稚的趣闻的科学时，你怎么办？如果你已经年长，你完全不希望跟那些吵吵嚷嚷的年轻学生混在一起，你又怎么办？
　　如今这个年代，你完全可以从Internet上得到所有知识。问题是，Internet上的垃圾太多了。你能从中筛选出那些真正有用而少的可怜的网页吗？我很清楚应该教什么东西给那些刚入门的学生。列出那些绝对必要的课程和课题的名称是很容易的，而这就是我下面已经完成了的。我的目的是搜集那些真正有用的论文和书籍所在的网页，最好是可下载的。通过这种方法，成为一个理论物理学家的成本不会超过一台可连接Internent的电脑、一个打印机、很多纸和笔。不幸的是，我不得不建议去买一些教材，但在此很难给出建议，或许将来的网站上会有。让我们先给自己一个最低限度。下面列出的科目是必须学习的。任何遗漏都将受到惩罚：失败。要相信我是对的：你不需要任何宗教式的笃信——去验证它吧。尽你所能，不断尝试。你将一次又一次地发现，那些人的工作的确是最聪明的。令人惊奇的是，最好的教材都有习题。去做习题，然后你会发现可以理解所有内容。你需要达到这种程度：发现大量的印刷错误、无足轻重的失误和重大差错，并想象你怎样以一种更聪明的方式撰写那些教材。
　　我可以告诉你我自己的经验。我很幸运，周围有那么多优秀的老师。这使我不致于误入歧途。这使我获得诺贝尔奖。但是我没有Interent。我将尝试做你的老师。这是一个艰巨的任务。我正在请求学生、同事和老师们帮助我改进这个网站。目前建立的这个网站仅仅针对那些力图成为理论物理学家的人，不是普通人，而是那些很棒的人，是那些下定决心要夺取诺贝尔奖的人。如果你是一个非常谦虚的人，很好，首先完成那些令人生厌的中学教育，并且循序渐进地吞下那些教育家和专业玩家如此混帐地把每一个细小的部分都仔细嚼碎了再喂给你的东西。这个网站针对雄心勃勃者。我确信任何人都能做到，只要你有足够的智力、兴趣和决心。
　　理论物理学就象一座摩天大楼。它有着初等数学和20世纪前经典物理学的坚实基础。虽说我们已拥有更多，也不要以为20世纪前的物理学是“不相干的”。在那些日子里，那坚实基础中保存着我们如今正享受着的知识。在你自己重新构建基础之前，不要去尝试造你自己的摩天大楼。摩天大楼的下面几层是由高等数学构成的，它们使经典物理学理论变得更加美丽动人。如果你想爬得更高，它们是必需的。因此，下面将列出其他一些课程。最后，如果你够疯而打算解决那些协调重力物理学与量子世界的极其困难的问题，你就拼了老命学习广义相对论、超弦理论、M-理论、Calabi-Yau流形，等等。这是摩天大楼目前的顶端。还有其他一些山峰，诸如玻色-爱因斯坦凝聚态、分数量子霍尔效应，等等。正如过去几年所显示的，这些也是角逐诺贝尔奖的好课题。一个必要的警告：即使你聪明绝顶，你还是会在某些地方卡死。你自己去网上冲浪吧。去发现更多。告诉我你的发现。如果这个网站对准备读大学的人有所帮助，如果激励了某些人，帮助一些人沿途而行，清除了他或她通往科学的道路，那么我认为这个网站就成功了。请让我知道。这里是课程列表。
　　记住，这个网站并不十分符合教育法，我使用颜色而不是令人分心的画面来避免使用文字以区分那些一点都不风趣的作者。同时，包含的课程也略微倾向于我的个人爱好。
　　课程列表，按照逻辑次序（并不是一切都必须依照这个次序，但是它大致的指明了了不同科目之间的逻辑关系。某些标题比另一些级别更高。）
　　·语言
　　·基本数学
　　·经典力学
　　·光学
　　·统计力学和热力学
　　·电子学
　　·电磁学
　　·量子力学
　　·原子和分子
　　·固体物理
　　·核物理
　　·等离子体物理
　　·高等数学
　　·狭义相对论
　　·高等量子力学
　　·唯象理论
　　·广义相对论
　　·量子场论
　　·弦论
　　更多资源
　　.ps文件是PostScript文件&。
　　（现在是初级阶段，这个网页还很不完整！）
　　英语是不可或缺的。如果你还不能熟练运用，就去学。你必须能够读、写、说，并且理解英语，但你在这里并不需要完美。这篇文章里的蹩脚英语就是我自己写的。这就够了。所有出版物都是英语的。要注意到英语书写能力的重要性。你很快就会希望发表你自己的成果。人们必须能够阅读和理解你的材料。
　　法语、德语、西班牙语和意大利语可能也有用，但他们不是必要的。他们并不靠近我们摩天大楼的基础，所以别担心。你确实需要希腊字母。希腊字母使用广泛。学习他们的名字，否则你演讲用到它们的时候会成为一个呆瓜。现在，开始给出严肃的材料。不要抱怨这些东西看起来很多。你休想无偿得到诺贝尔奖，而且记住，所有这些加在一起至少要需要我们的学生进行近5年的勤奋学习（至少有一个读者对这个说明表示惊讶，声称他/她绝不可能在5年里熟练掌握这些内容；的确，我是对那些计划在这个学习上花很多时间的人说的）。现在假定仍有可待开发的智力，因为普通学生可以在教师的协助下熟习之。做习题是必要的。要力图比作者更聪明，但是在全部学会之前千万别写信告诉我你那非主流理论；如果你彻底学会了，你将发现那些作者毕竟不蠢。
现在，首先要学的是：
　　你喜欢数字、加法、减法、平方根等等么？
*西德克萨斯A&M大学《代数入门》*：
*西德克萨斯A&M大学《代数进阶》*： ... t_algebra/index.htm
　　·自然数：1，2，3，……
　　·整数：……，-3，-2，-1，0，1，2，……
　　·有理数（分数）：1/4，1/2，3/4，，……
　　·实数：Sqrt(2) = 1.4142135……，pi = 3.……，e = 2.7182818……
　　·复数：2+3i，eia = cos(a) + i*sin(a)，……它们非常重要！
Dave E. Joyce的三角函数课程：
这是必须的：James Binney教授的复数课程：
肯塔基K.Kubota的“初等数学一览”：
还可参看Chris Pope的讲义：
亚特兰大G. Cain的复平面、柯西定理和线积分：
　　集合论：开集，紧致空间，拓扑。你可能会惊讶，它们在物理学中的确扮演了角色！
　　代数方程：求近值方法。级数展开：泰勒级数。解复数方程。三角函数：sin(2x) = 2*sin(x)*cos(x)，等等。
　　无穷小。微分。初等函数的微分（sin，cos，exp）。
　　积分。初等函数的积分。微分方程。线性方程。
　　傅里叶变换。复数的应用。级数的收敛。
　　复空间。柯西定理和线积分（现在这些很有趣）。
　　Γ函数（享受在学习其性质时的乐趣）。
　　高斯积分。概率论。
　　偏微分方程。狄里克莱和诺依曼边界条件。
　　这些是针对初学者的。有些内容可能成为一个完整的讲座课程。这些内容大多是物理学理论中必须的。你开始学习后面的内容时并不需要学完所有这些课程，但记住以后要回来完成那些你第一次漏掉的。
一个来自哈佛的很棒的笔记：
德克萨斯Austin大学R. Fitzpatrick的一个经典分析动力学的进阶课程：
　　·静力学（力，张力）；流体静力学。牛顿定律。
　　·行星椭圆轨道。多体系统。
　　·作用量原理。哈密尔顿方程。拉格朗日方程。（不要跳过，极其重要！）
　　·谐振子。摆。
　　·泊松括号。
　　·波动方程。液体和气体。纳维-斯托克斯方程。粘滞性和摩擦。
A. A. Louro的光学讲义：
　　·折射和反射。
　　·透镜和镜子。
　　·望远镜和显微镜。
　　·波的传播初步。
　　·多普勒效应。
　　·波的叠加的惠更斯原理。
　　·波前。
　　·焦散面。
统计力学和热力学
Alfred Huan的统计力学课程：
Donald B. Melrose教授的热力学讲义：
　　·热力学第一、第二和第三定律。
　　·玻尔兹曼分布。
　　·卡诺循环。熵。热机。
　　·相变。热力学模型。
　　·伊辛模型（把求解2维伊辛模型的技术推迟到后面）。
　　·普朗克辐射定律（作为量子力学的序曲）。
（只有一些非常基本的电路方面的东西）
　　·欧姆定律，电容，电感，用复数计算他们的效应。
　　·晶体管，电子管（其工作原理以后再学）。
James Kelly《自然科学学生的数学必读》： ... ssentialMathematica
Angus MacKinnon《计算机物理》：
W.J.Spence《电磁学》：
Bo Thide的高等电磁场理论习题：
Jackson的习题答案：
　　即便是纯粹的理论家也可能对计算物理的某些方面感兴趣。
　　电磁学的麦克斯韦理论:
　　·各向同性的和各向异性的
　　介质中的麦克斯韦定律。边界。求解以下方程：
　　·真空和各向同性介质（电磁波）
　　·箱体（波导）
　　·边界（折射和反射）
　　矢势和规范不变性（极其重要）
　　电磁波的发射和接收（天线）
　　光的散射
量子力学（非相对论性）
Michael Fowler的量子力学和狭义相对论入门：
曼彻斯特Niels Walet的量子力学讲义：
　　·玻尔的原子论
　　·德·布罗意关系（能量-频率，动量-波长）
　　·薛定谔方程（带电磁场）
　　·欧伦菲斯特定理
　　·箱体中的单粒子
　　·氢原子，详细的求解。塞曼效应。斯塔克效应。
　　·量子谐振子。
　　·算子：能量，动量，角动量，产生和湮灭算子。
　　·其变换规则。
　　·量子力学散射初步。S矩阵。放射性衰变。
原子和分子
　　·化学键
　　·轨道
　　·原子和分子光谱
　　·光的发射和吸收
　　·量子选择规则
　　·磁矩
固体物理：Chetan Nayak的笔记（UCLA）：
　　·晶格
　　·布拉格反射
　　·电介常数和反磁性常数
　　·布洛赫谱
　　·费米能级
　　·导体，半导体和绝缘体
　　·比热
　　·电子和空穴
　　·晶体管
　　·超导
　　·霍尔效应
　　·同位素
　　·放射性
　　·裂变和聚变
　　·液滴模型
　　·核的量子数
　　·幻数核
　　·同位旋
　　·汤川理论
等离子体物理
　　·磁流体力学
　　·阿尔文波
参看佛吉尼亚John Heinbockel：
参看Chr. Pope: Methods2&：
数学习题集：
G.'t Hooft的《李群》（荷兰文+习题）：
关于李群还可参看Chr. Pope讲义最后一章（“广义相对论”后面）
《特殊函数和多项式》（理解那些原理即可）：
　　·群论，群的线性表示
　　·李群理论
　　·矢量和张量
　　·更多的求解（偏）微分方程和积分方程的技巧
　　·极值原理和基于它的近似技巧
　　·差分方程
　　·母函数
　　·希尔伯特空间
　　·泛函积分初步
狭义相对论
Peter Dunsby的张量和狭义相对论课程：
　　·洛仑兹变换
　　·洛仑兹收缩，时间膨胀
　　·E = mc2
　　·4维矢量和4维张量
　　·麦克斯韦场的变换规则
　　·相对论多普勒效应
高等量子力学
密歇根州立大学高等量子力学笔记：
　　·希尔伯特空间
　　·原子跃迁
　　·光的发射和吸收
　　·受激发射
　　·密度矩阵
　　·量子力学的解释
　　·贝尔不等式
　　·过渡到相对论性量子力学：狄拉克方程，精细结构
　　·电子和正电子
　　·超导的BCS理论
　　·量子霍尔效应
　　·高等散射理论
　　·色散关系
　　·微扰展开
　　·WKB近似，极值原理
　　·玻色*爱因斯坦凝聚态
　　·超流氦
　　亚原子粒子（介子，重子，光子，轻子，夸克）和宇宙射线；材料性质和化学；核同位素；相变；天体物理（行星系，恒星，星系，红移，超新星）；宇宙学（宇宙学模型，暴涨宇宙论，微波背景辐射）；测量技术。
广义相对论
G. 't Hooft的入门和习题：
选读：Sean M. Carrol的广义相对论讲义：
Chr. Pope《几何和群论》：
　　·度规张量
　　·时空曲率
　　·爱因斯坦引力方程
　　·斯瓦兹察尔德黑洞
　　·雷斯纳-诺斯陶姆黑洞
　　·近日点位移
　　·引力透镜
　　·宇宙模型
　　·引力辐射
Pierre van Baal的量子场论笔记：
G. 't Hooft的《量子场论的概念基础》：
《科学哲学手册》中的一章：
磁单极和瞬子：
　　·经典场：标量场，狄拉克旋量，杨-米尔斯矢量场。
　　·相互作用，微扰展开。自发对称性破缺，戈德斯通方法，黑格斯机制。
　　·粒子与场：福克空间。反粒子。费曼规则。π介子和核子的盖尔曼-李维Σ模型。圈图。么正性、因果律和色散关系。重正化（泡利-维拉斯；维数重正化）。量子规范理论：规范不变，法捷耶夫-波波夫行列式，斯拉夫诺夫恒等式，BRST对称。重正化群。渐进自由。
　　·孤立子，斯卡米子。磁单极和瞬子。夸克永久禁闭机制。1/N展开。算符乘积展开。贝瑟-萨佩特方程。标准模型的建立。P和CP破坏。CPT定理。自旋和统计的联系。超对称。
入门和习题：
一个超弦大众网站：
更多的网上讲义可以在这里找到： ... s_lecture_notes.htm
有许多理论物理各种课题的好书，这里列出少量书目：
·J.B. Marion & W.F. Hornyak, Principles of Physics, Saunders College Publishing, 1984, ISBN 0-03-
·H. Margenau and G.M. Murphy, The Mathematics of Physics and Chemistry, D. v.Nostrand Comp.
·R. Baker, Linear Algebra, Rinton Press
·L. E. Reichl: A Modern Course in Statistical Physics, 2nd ed.
·R. K. Pathria: Statistical Mechanics
·M. Plischke & B. Bergesen: Equilibrium Statistical Physics
·L. D. Landau & E. M. Lifshitz: Statistical Physics, Part 1
·S.-K. Ma, Statistical Mechanics, World Scientific
·J.D. Jackson, Classical Electrodynamics, 3rd ed., Wiley & Sons.
·A. Das & A.C. Melissinos, Quantum mechanics, Gordon & Breach
·A.S. Davydov, Quantum Mechanics. Pergamon Press
·E. Merzbacher, Quantum Mechanics, Wiley & Sons
·R. Shankar, Principles of Quantum Mechanics, Plenum
·J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley
·B. de Wit & J. Smith, Field Theory in Particle Physics, North-Holland
·I.J.R. Aitchison & A.J.G. Hey, Gauge Theories in Particles Physics, Adam Hilger
·L.H. Ryder, Quantum Field Theory, Cambridge Univ. Press
·C. Itzykson & J.-B. Zuber, Quantum Field Theory, McGraw-Hill.
·J.B. Hartle, Gravity, An Introduction to Einstein's General Relativity, Addison Wesley, 2003.
·T.-P. Cheng, Relativity, Gravitation and Cosmology, A Basic Introduction, Oxford Univ. Press, 2005.
·Barton Zwiebach, A First Course in String Theory, Cambridge Univ. Press, 2004
·M.B. Green, J.H. Schwarz & E. Witten, Superstring theory, Vols. I & II, Cambridge Univ. Press
·J. Polchinski, String Theory, Vols. I & II, Cambridge Univ. Press.
其它有用的教材书目：
（其中很多只是消遣读物，而不是理解世界之必不可少的。）
已经有了一些反响。我要感谢：Rob van Linden、Robert Tough、Thuy Nguyen、Tina Witham、Jerry Blair、Jonathan Martin以及其他人。
　　Hisham Kotry先生提出了一个重要的问题：
　　“您概括了有潜力的学生穿越大学物理之丛林的途经……两年前，我决定按照来自您主页上的名校教学大纲和建议自学理论物理，目前已略有所成，但我的疑惑是下一步怎么办？引用一下您以前的主页：‘简而言之，是为了那些决定以毕生精力研究理论物理学的人。’您知道是否有人没有大学文凭，却终身从事于某个物理领域或者在研究所中花自己的时间进行研究？”
　　遗憾的是，回答这个问题不那么容易。我的回答是：
　　说到底，无论你是否喜欢，如果你希望依靠理论物理方面的职业养活自己，你还是必须获得某大学的文凭。关注一下《本校硕士课程要求》（）是有价值的。我不清楚你的学历，但我认为，有志者事竞成。
　　这不是空话，是很现实的。还可以给的建议是，一旦你认为自己自学完成，就不要等待。你必须让自己的能力接受检验，以便你得到应得的认可。而且，我经常遇到卡在某一点上的人。一个人只有处于与教师和同事之间强烈的互动之中，才能使自己摆脱困境。我还没有见到任何人能够缺乏辅导而只凭他/她自己就完成所有的学业。如果你真的认为自己在学习中已经达到一个很高的水平，你可以尝试一下在你感兴趣的颗题上获得学校、研究组织和工业界的认可。
　　3/04/06：来自印第安那州Bloomington（译注：美国印第安那大学所在地）的John Glasscock发来的消息：
　　我目前唯一知道的人是多伦多大学的John Moffatt，他是伦敦帝国科技学院Abdus Salam的学生。（译注：Abdus Salam，，1977年诺贝尔物理学奖得主。）他原先是巴黎的一个油漆工，没有大学文凭，自学成才，与爱因斯坦通信，然后基于他在IC卡上非凡的独创性工作而被认可。（来源：Joao Magueijo, _Faster than the Speed of Light_. Perseus Publishing, Cambridge, MA. 2003.）
　　来自Alvaro V&liz的建议而给出更多的讲义：
　　1、The archimedeans（）网页：上面有许多剑桥的物理和数学讲义。
　　2、David Tong（DAMTP）的经典力学（）我发现这些讲义好棒。
　　3、瑞典乌普萨拉Bo Thide的讲义（）电磁学理论。
　　4、Angel Uranga的弦论讲义（ ... anga/firstpage.html）。
　　5、我还发现了MIT的开放式教程（）。Lewin的基础物理讲义非常好（有视频）。
　　6、佛吉尼亚Michael Fowler的量子力学讲义（）。
　　（未经Gerard 't Hooft的检查。）
HOW to BECOME a GOOD THEORETICAL
This is a web site (still under
construction) for young students - and anyone
else - who are (like me) thrilled by the challenges posed by real
science, and who are - like me - determined to use their brains to
discover new things about the physical world that we are living in.
In short, it is for all those who decided to study theoretical
physics, in their own time.
It so often happens that I receive mail -
well-intended but totally useless - by amateur physicists who
believe to have solved the world. They believe this, only because
they understand totally nothing about the real way problems are
solved in Modern Physics. If you really want to contribute to our
theoretical understanding of physical laws - and it is an exciting
experience if you succeed! - there are many things you need to
know. First of all, be serious about it. All necessary science
courses are taught at Universities, so, naturally, the first thing
you should do is have yourself admitted at a University and absorb
everything you can. But what if you are still young, at School, and
before being admitted at a University, you have to endure the
childish anecdotes that they call science there? What if you are
older, and you are not at all looking forward to join those noisy
crowds of young students ?
It should be possible, these days, to collect
all knowledge you need from the internet. Problem then is, there is
so much junk on the internet. Is it possible to weed out those very
rare pages that may really be of use? I know exactly what should be
taught to the beginning student. The names and topics of the
absolutely necessary lecture courses are easy to list, and this is
what I have done below. It is my intention to search on the web
where the really useful papers and books are, preferably
downloadable as well. This way, the costs of becoming a theoretical
physicist should not exceed much the price of a computer with
internet connection, a printer, and lots of paper and pens.
Unfortunately, I still have to recommend to buy text books as well,
but it is harde perhaps in a future site.
Let's first limit ourselves to the absolute minimum. The subjects
listed below must be studied. Any omission will be punished:
failure. Do get me right: you don't have to believe anything you
read on faith - check it. Try alternative approaches, as many as
you can. You will discover, time and again, that really what those
guys did indeed was the smartest thing possible. Amazing. the best
of the texts come with exercises. Do them. find out that you can
understand everything. Try to reach the stage that you discover the
numerous misprints, tiny mistakes as well as more important errors,
and imagine how you would write those texts in a smarter way.
I can tell you of my own experiences. I had the
extreme luck of having excellent teachers around me. That helps one
from running astray. It helped me all the way to earn a Nobel
Prize. But I didn't have internet. I am going to try to be your
teacher. It is a formidable task. I am asking students, colleagues,
teachers to help me improve this site. It is presently set up only
for those who wish to become theoretical physicists, not just
ordinary ones, but the very best, those who are fully determined to
earn their own Nobel Prize. If you are more modest than that, well,
finish those lousy schools first and follow the regular routes
provided by educators and specialized -gogues who are so damn
carefully chewing all those tiny portions before feeding them to
you. This is a site for ambitious people. I am sure that anyone can
do this, if one is gifted with a certain amount of intelligence,
interest and determination.
Theoretical Physics is
like a sky scraper. It has solid foundations in elementary
mathematics and notions of classical (pre-20th century) physics.
Don't think that pre-20th century physics is "irrelevant" since now
we have so much more. In those days, the solid foundations were
laid of the knowledge that we enjoy now. Don't try to construct
your sky scraper without first reconstructing these foundations
yourself. The first few floors of our skyscraper consist of
advanced mathematical formalisms that turn the Classical Physics
theories into beauties of their own. They are needed if you want to
go higher than that. So, next come many of the other subjects
listed below. Finally, if you are mad enough that you want to solve
those tremendously perplexing problems of reconciling gravitational
physics with the quantum world, you end up studying general
relativity, superstring theory, M-theory, Calabi-Yau
compactification and so on. That's presently the top of the sky
scraper. There are other peaks such as Bose-Einstein condensation,
fractional Hall effect, and more. Also good for Nobel Prizes, as
the past years have shown. A warning is called for: even if you are
extremely smart, you are still likely to get stuck somewhere. Surf
the net yourself. Find more. Tell me about what you found. If this
site has been of any help to someone while preparing for a
University study, if this has motivated someone, helped someone
along the way, and smoothened his or her path towards science, then
I call this site successful. Please let me know. Here is the
Note that this site NOT meant to be very
pedagogical. I avoid texts with lots of colorful but distracting
pictures from authors who try hard to be funny. Also, the subjects
included are somewhat focused towards my own interests.
LIST OF SUBJECTS, IN LOGICAL
ORDER (not everything has to be done in this order, but this
approximately indicates the logical coherence of the various
subjects. Some notes are at a higher level than others).
The .ps files are PostScript files &#65533;.
(In this initial phase this page is still incomplete!)
Languages:English is a
prerequisite. If you haven't mastered it yet, learn it. You must be
able to read, write, speak and understand English, but you don't
have to be perfect here. The lousy English used in this text is
mine. That's enough. All publications are in English. Note the
importance of being able to write in English. Sooner or later you
will wish to publish your results. People must be able to read and
understand your stuff.
French, German, Spanish and Italian may be useful too, but they
are not at all necessary. They are nowhere near the foundations of
our sky-scraper, so don't worry. You do need the Greek alphabet.
Greek letters are used a lot. Learn their names, otherwise you make
a fool of yourself when giving an oral presentation. Now, here
begins the serious stuff. Don't complain that it looks like being a
lot. You won't get your Nobel Prize for free, and remember, all of
this together takes our students at least 5 years of intense study
(at least one reader was surprised at this statement, saying that
(s)he would never master this in 5 indeed, I am addressing
people who plan to spend most of their time to this study). More
than rudimentary intelligence is assumed to be present, because
ordinary students can master this material only when assisted by
patient teachers. It is necessary to do exercises. Some of the
texts come with exercises. Do them, or better, invent your own
exercises. Try to outsmart the authors, but please refrain from
mailing to me your alternative theories until you have studied the
if you do this well you will discover that many of
these authors were not so stupid after all.
Now, first things first :
Primary Mathematics:Are you
comfortable with numbers, adding, subtracting, square roots, etc.?
** (West Texas A&M)
** (West Texas A&M)
Natural numbers: 1, 2, 3, ...
Integers: ..., -3, -2, -1, 0, 1, 2, ...
Rational numbers (fractions): &frac14;, &frac12;, &frac34;,&
23791 / 773, ...
Real numbers: Sqrt(2) = 1.4142135... ,&
π& = 3.... , e = 2.7182818...,
Complex numbers: 2+3i, eia=
cos(a) + i sin( a), ... they are very
important!
This is a must:
(K.Kubota, Kentucky)
See also Chris Pope's lecture notes:
Cain, Atlanta)
Set theory: open sets, compact spaces.
Topology.You may be surprised to learn that they do play a role
indeed in physics!
Algebraic equations. Approximation techniques. Series
expansions: the Taylor series. Solving equations with complex
numbers. Trigonometry: sin(2x)=2sin x cos x,
Infinitesimals. Differentiation. Differentiate basic functions
(sin, cos, exp). Integration. Integrate basic functions, when
possible. Differential equations. Linear equations.
The Fourier transformation. The use of complex numbers. Convergence
of series.
The complex plane. Cauchy theorems and contour integration (now
this is fun).
The Gamma function (enjoy studying its properties).
Gaussian integrals. Probability theory.
Partial differential equations. Dirichlet and Neumann boundary
conditions.
This is for starters. Some of these topics actually come as
entire lecture courses. Much of those are essential ingredients of
theories in Physics. You don't have to finish it all before
beginning with what follows next, but remember to return to those
subjects skipped during the first round.
Classical Mechanics:
Static mechanics (forces, tension); hydrostatics. Newton's
The elliptical orbits of planets. The many-body system.
The action principle. Hamilton's equations. The Lagrangean.
(Don't skip - extremely important!)
The harmonic oscillator. The pendulum.
Poisson's brackets.
Wave equations. Liquids and gases. The Navier-Stokes equations.
Viscosity and friction.
fraction and reflection.
lenses and mirrors.
The telescope and the microscope.
Introduction to wave propagation.
Doppler effect.
Huijgens' principle of wave superposition.
Wave fronts.
Statistical Mechanics and
Thermodynamics:
The first, second and third laws of thermodynamics.
The Boltzmann distribution.
The Carnot cycle. Entropy. Heat engines.
Phase transitions. Thermodynamical models.
The Ising Model (postpone techniques to solve the 2-dimensional
Ising Model to later).
Planck's radiation law (as a prelude to Quantum Mechanics)
Electronics:
(Only some very basic things about electronic circuits)
Ohm's law, capacitors, inductors, using complex numbers to
calculate their effects.
Transistors, diodes (how these actually work comes later).
Electromagnetism:
Worked out exercises from Jackson's book,
Maxwell's Theory for electromagnetism
homogeneous and inhomogeneous
Maxwell's laws in a medium. Boundaries. Solving the equations in:
vacumm and homogeneous medium (electromagnetic waves)
in a box (wave guides)
at boundaries (fraction and reflection)
The vector potential and gauge invariance (extremely
important)
emission and absorption on EM waves (antenna)
light scattering against objects.
Computational Physics :
Even the pure sang theorist may be interested in some aspects of
Computational physics.
Quantum Mechanics
(Non-relativistic):
(Manchester)
Bohr's atom.
DeBroglie's relations (Energy-frequency, momentum-wave
Schr&#65533;dinger's equation (with electric potential and magnetic
Ehrenfest's theorem.
A particle in a box.
The hydrogen atom, solved systematically. The Zeeman
effect.Stark effect.
The quantum harmonic oscillator.
Operators: energy, momentum, angular momentum, creation and
annihilation operators.
Their commutation rules.
Introduction to quantum mechanical scattering. The
S-matrix. Radio-active decay.
Atoms and Molecules:
Chemical binding
Atomic and molecular spectra
Emission and absorption of light.
Quantum selection rules
Magnetic moments.
Solid State Physics:
Crystal groups
Bragg reflection
Dielectric and diamagnetic constants
Bloch spectra
Fermi level
Conductors, semiconductors and insulators
Specific heat
Electrons and holes
The transistor
Supraconductivity
Hall effect.
Nuclear Physics
Radio-activity
Fission and fusion
Droplet model
Nuclear quantum numbers
Magic nuclei
Yukawa theory
Plasma physics:
magneto-hydrodynamics
Alfv&#65533;n waves
Advanced Mathematics:
See Chr. Pope: &#65533;
G.'t Hooft:
For Lie Groups, see also the last section of Chr. Pope's
lectures (under "General Relativity")
(just understand the
principles)
Group theory, and the linear representations of groups
Lie group theory
Vectors and tensors
More techniques to solve (partial) differential and integral
Extremum principle and approximation techniques based on
Difference equations
Generating functions
Hilbert space
Introduction to the functional integral
Special Relativity
The Lorentz transformation
Lorentz contraction, time dilatation
4-vectors and 4-tensors
Transformation rules for the Maxwell field
Relativistic Doppler effect
Advanced Quantum Mechanics:
Hilbert space
Atomic transitions
Emission and absorption of light
Stimulated emission
Density matrix
Interpretation of QM
The Bell inequalities
Towards relativistic QM: The Dirac equation, finestructure
Electrons and positrons
BCS theory for supraconductivity
Quantum Hall effect
Advanced scattering theory
Dispersion relations
Perturbation expansion
WKB approximation, Extremum principle
Bose-Einstein condensation
Superliquid helium
Phenomenology:
subatomic particles (mesons, baryons, photons, leptons, quarks)
property of mat nuclear
astrophysics (planetary system, stars,
galaxies, red shifts, supernovae); cosmology (cosmological models,
inflationary universe theories, microwave background radiation);
detection techniques.
General Relativity:
by G. 't Hooft
Alternative:
Chr. Pope, Geometry and Group Theory, ,
The metric tensor
Space-time curvature
Einstein's gravity equation
The Schwarzschild black hole
Reissner-Nordstr&#65533;m black hole
Periastron shift
Gravitational lensing
Cosmological models
Gravitational radiation
Quantum Field Theory:
by G. 't Hooft
a chapter in
Classical fields: Scalar, Dirac-spinor, Yang-Mills vector
Interactions, perturbation expansion. Spontaneous symmetry
breaking, Goldstone mode, Higgs mechanism.
Particles and fields: Fock space. Antiparticles. Feynman rules.
The Gell-Mann-L&#65533;vy sigma model for pions and nuclei. Loop diagrams.
Unitarity, Causality and dispersion relations. Renormalization
(Pauli-V dimensional ren.) Quantum gauge theory: Gauge
fixing, Faddeev-Popov determinant, Slavnov identities, BRST
symmetry. The renormalization group. Asymptotic freedom.
Solitons, Skyrmions. Magnetic monopoles and instantons.
Permanent quark confinement mechanism. The 1/N expansion.
Operator product expansion. Bethe-Salpeter equation. Construction
of the Standard Model. P and CP violation. The
CPT theorem. Spin and statistics connection.
Supersymmetry.
Superstring Theory:
There are many more
to be found on the web.
There are numerous good books on all sorts of topics in
Theoretical Physics.
Just to name a few:
Mechanics:
Classical Mechanics - 3rd ed. - Goldstein, Poole
Classical dynamics: a contemporary approach - Jorge V. Jos&#65533;,
Eugene J. Saletan
Classical Mechanics - Systems of Particles and Hamiltonian
Dynamics - W. Greiner
Mathematical Methods of Classical Mechanics, 2nd ed. - V.I.
Mechanics 3rd ed. - L. Landau, E. Lifshitz
Statistical
Mechanics:
L. E. Reichl: A Modern Course in Statistical Physics, 2nd
R. K. Pathria: Statistical Mechanics
M. Plischke & B. Bergesen: Equilibrium
Statistical Physics
L. D. Landau & E. M. Lifshitz: Statistical
Physics, Part 1
S.-K. Ma, Statistical Mechanics, World Scientific
Mechanics:
Quantum Mechanics - an Introduction, 4th ed. - W. Greiner
R. Shankar, Principles of Quantum Mechanics, Plenum
Quantum Mechanics - Symmetries 2nd ed. - W. Greiner, B.
Quantum Mechanics - Vol 1&2 -
Cohen-Tannoudji
J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley
Electrodynamics:
J.D. Jackson, Classical Electrodynamics, 3rd ed., Wiley
Electromagnetic Fields And Waves - lorrain and corson
Classical Electrodynamics - W. Greiner
Introduction to Electrodynamics - D. Griffiths
Quantum Electrodynamics - 3rd ed., - W. Greiner, J. Reinhardt
Principles of Optics - M.Born, E. Wolf
Principles Of Nonlinear Optics - Y. R. Shen
Thermodynamics:
Thermodynamics and an Introduction to Thermostatistics 2ed - H.
Thermodynamics and statistical mechanics - Greiner, Neise,
Solid State
Solid State Physics - Ashcroft, Neil W, Mermin, David N
Introduction to Solid State Physics 7th edition- Kittel,
Relativity:
Classical Mechanics - Point Particles And Relativity - W.
Introduction to the theory of relativity and the principles of
modern physics - H. Yilmaz
Relativity:
J.B. Hartle, , An
Introduction to Einstein's General Relativity, , 2003.
T.-P. Cheng, Relativity, Gravitation and Cosmology, A Basic
Introduction, Oxford Univ. Press, 2005.
Introduction to Elementary Particles - D. Griffiths
Fundamentals in Nuclear Physics - From Nuclear Structure to
Cosmology - Basdevant, Rich, Spiro
B. de Wit & J. Smith, Field Theory in Particle
Physics, North-Holland
C. Itzykson & J.-B. Zuber, Quantum Field
Theory, McGraw-Hill.
Barton Zwiebach, A First Course in String Theory, Cambridge
Univ. Press, 2004
M.B. Green, J.H. Schwarz & E. Witten,
Superstring theory, Vols. I & II, Cambridge Univ.
Cosmology:
An Introduction to cosmology, 3rd Ed & Roos
Relativity, thermodynamics, and cosmology - Tolman R.C.
J.B. Marion & W.F. Hornyak, Principles of
Physics, Saunders College Publishing, 1984, ISBN 0-03-
H. Margenau and G.M. Murphy, The Mathematics of Physics and
Chemistry, D. v.Nostrand Comp.
R. Baker, Linear Algebra, Rinton Press
Find lists of other useful textbooks here: ,
(most of these are rather for amusement than being essential for
understanding the World),
or a little bit more seriously: .
There already is some response. I thank: Rob van Linden, Robert
Tough, Thuy Nguyen, Tina Witham, Jerry Blair, Jonathan Martin,
David Cuthbertson, Trent Strong, and many others.
Mr. Hisham Kotry came with an important
"...You sketch the path for potential students through the
forest of college level physics... Two years ago I decided to
self-study theoretical physics by following the syllabus of a
renown university and the advice from your page and now I'm
half-way through the journey but I was wondering about what happens
next? Quoting you from the former page "In short, it is for all
those who decided to study theoretical physics, in their own
time.", Do you know of anyone who got tenure at a physics
department or any research institute based on studies he did in his
own time without holding a university degree?"
This is not so easy to answer, unfortunately. What I can say,
Eventually, whether you like it or not, you will have to obtain
some University degree, if you wish a self-supporting career in
theoretical Physics. One possibility is to follow a . I don't know about your
qualifications, but I suspect that, with enough determination, you
may be able to comply.
This is not a burocratic argument but a very practical one. It
is also advisable not to wait until you think your self-study is
completed. You must allow your abilities to be tested, so that you
get the recognition that you may well deserve. Also, I frequently
meet people who get stuck at some point. Only by intense
interactions with teachers and peers one can help oneself across
such barriers. I have not yet met anyone who could do the entire
study all by him/herself without any guidance. If you really think
you have reached a professional level in your studies, you can try
to get admitted to schools, conferences and workshops in topics of
your interest.
3/04/06: Message received from John Glasscock, Bloomington,
The only one I know of currently is John Moffatt at U Toronto, who
was a student of Abdus Salam at Imperial College, London. He
started life as a painter in Paris, had no undergraduate degree,
taught himself, corresponded with Einstein, and was admitted, based
on his demonstrated original work, at IC. (Source: Jo&#65533;o Magueijo,
_Faster than the Speed of Light_. Perseus Publishing, Cambridge,
MA. 2003.)
Suggestions for further lecture notes from Alvaro V&#65533;liz:
webpage: It
has a lot of lecture notes in Physics and Mathematics from Part I
and II from Cambridge.
I found these lectures fascinating.
in electromagnetic theory.
5. I found also extremely helpful
lectures in basic Physics are terrific (in video).
(not checked, G. 't H.)
I thank Aldemar Torres Valderrama for his assistance in
updating and renewing numerous links on this page.
& Note that .ps files are PostScript files, so defend yourself
against Microsoft PaintShop, that often wants to appropriate .ps
files. PostScript files are read using GhostView (gsview)
已投稿到：
以上网友发言只代表其个人观点，不代表新浪网的观点或立场。