Lectures on Quantum Mechanics

by Paul A.M. Dirac

Four concise, brilliant lectures on mathematical methods by the Nobel Laureate and quantum pioneer begin with an introduction to visualizing quantum theory through the use of classical mechanics. The remaining lectures build on that idea, examining the possibility of building a relativistic quantum theory on curved surfaces or flat surfaces.

Genres: Physics, Science, Textbooks, Quantum Mechanics, Mathematics, Nonfiction

87 pages, Paperback

First published January 1, 1964

About the author

Paul Adrien Maurice Dirac was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. He was the Lucasian Professor of Mathematics at the University of Cambridge, a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.

Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.

Reviews

[Erickson · Rating 4 out of 5]

This book is "hard" because it is too terse in a real sense. With only 90 pages or so Dirac managed to perform quantization via Hamiltonian formalism. It is to be understood that the readers are experts in the field or researchers well acquainted with some aspects of quantum field theory already. This is further supported by the fact that in final chapter Dirac seems to assume reader has heard of Born-Infeld electrodynamics. I am unfortunately only fourth-year undergraduate with somewhat ill-developed fundamentals.

However, this book can be quite a good eye-opener on some fundamental concepts. In chapter 1 and 2, his discussion on classical Hamiltonian and constraint equations make it clear what constraint equations mean in physics and how it translates to e.g. gauge fixing, Lagrange multiplier-type of constraint enforcement, among others. While classification of constraints into 4 types (primary, secondary, first class, second class) can be confusing, the discussion on constraint equations in Hamiltonian formalism is illuminating - since even in modern understanding of general relativity (and electrodynamics), the constraint equations and evolution equations are exactly what the ADM decomposition and Maxwell's equations are.

Although solid insights are probably manifest only after second or third reading, it is still worth reading despite the likelihood to be out of date compared to present-day (2016) developments in quantum field theory. This is especially the case when the book is only 90 (small-sized) pages thick.

[Chris Marks · Rating 1 out of 5]

Lectures in the worst sense of that word. Dry derivations of equations with little actual physics. Dirac and the results are historically important, but there must be better ways to learn this stuff. Perhaps interesting as a textbook, with a knowledgeable teacher to provide some much needed context and add some life to the story. All of this was made even more challenging by the difficult to read equations in the Kindle edition; especially not recommended in that format.

Viewed another way, and in a printed format, the book might be quite good and useful [to budding theoretical physicists]. I don't really disagree with Erickson's four-star review, as far as it goes.

[Roberto Rigolin F Lopes · Rating 4 out of 5]

We are in 1964, Dirac is building a relativistic quantum theory starting from classical mechanics. Just four lectures.But he assumes that you know a great deal of physics so this is a good brain workout for curious readers; anyone can survive few short lectures. He lost me several times but the text is warm and he took the time to explain isomorphisms between abstractions and its physical meanings. This is priceless against the usual dullness of textbooks. There is also a sense of surprise because he is never sure that his quantum theory will hold in the end. Often saying that we need a bit of luck to match the consistency conditions. It didn't because of "quite formidable difficulties". Take away: his notation is neat/elegant and "infinity usually does lead to trouble".

[Kyle · Rating 3 out of 5]

Reading this book somehow cured me of my armchair physicist fascination with quantum mechanics: prior to read these lectures, I had the awe-struck feeling that any part of this theory could reveal the mysteries of the universe. The plain-spoken and formula-heavy presentation of curved and flat surfaces seemed to have less and less connection to any part of the universe, the more he went on. I’d like to believe that the Hamiltonian Method will somehow be a puzzle piece fitting into an implicate order, but if it doesn’t and no doubt since Dirac’s day the whole theory has been replaced and improved upon numerous times, I’ll never know.

[Lori · Rating 5 out of 5]

Classic example of one of those small books that you think will be a breeze to read, but then wind up taking up much more time than you initially thought. True testament to the genius of Paul Dirac.

[Manmohan Dash · Rating 5 out of 5]

To understand the formalism of quantization, a succinct technical exposition from the genius.

[Jose Brox · Rating 4 out of 5]

I just read the first two lectures, which are the more elementary ones. Dirac introduces, in an abstract and mathematical setting, the method of quantization of a classical system by means of the description of its classical Hamiltonian (which is then used in Schrödinger's equation), starting from the action (time) integral of the Lagrangian, in order to get a relativistic version of the quantized model. Poisson brackets are introduced to get simpler expressions. Emphasis is put on the classification and use of the restrictions applied to the variables. The development is done for a finite number of degrees of freedom, but (as Dirac states) it can straightly adapted for a field theory by taking the limit to infinite (changing sums by integrals and the like). An example based on electromagnetism is given. The exposition is quite clear (given its conciseness and the aridity of the subject), but I think it could be helped by introducing the modern theory of abstract Lie algebras.

[Mark Petkov · Rating 5 out of 5]

Stunning. Dirac at its best revealing some of the most intrinsic concepts of physics through elegant mathematics.

[Mi Lia · Rating 5 out of 5]

One can only but look at awe at the work of this genius.

A must have for anyone that would like to come closer to the mind of this important englishman.

[Josh Issa · Rating 3 out of 5]

tbh I don’t think I followed the whole time // prob need to re-read in a few months

[Juan Falgueras cano · Rating 2 out of 5]

It has disappointed my expectations since I wanted to read something so philosophical and profound like Schrödinger "What is life" but this book enters straight to some mathematical questions from a Dirac speech, very specialised

[Innay Eza]

very good

[Bharat Kumar · Rating 3 out of 5]

i would like research on quantum mechanics that,s why i would like to read some standard books which help me to understand the subject more.