math and physics play

Notes for ece1228 (Electromagnetic Theory) now in book form on Amazon.

September 26, 2020 math and physics play No comments ,

My notes for ece1228 (Electromagnetic Theory) are now available in book form on Amazon.

This version omits all assigned problem solutions (but includes some self-generated problem solutions.)  As such, it is very short.  I published it so that I could get a copy (of the non-redacted version) for myself , but in the unlikely chance that somebody else is interested I’ve left the redacted version in published state (available very cheaply.)  Feel free to contact me for the full (pdf) version if you are not taking the course (and don’t intend to.)

The official course description at the time was:

Fundamentals: Maxwell’s equations, constitutive relations and boundary conditions, wave polarization. Field representations: potentials, Green’s functions and integral equations. Theorems and concepts: duality, uniqueness, images, equivalence, reciprocity and Babinet’s principles. Plane, cylindrical and spherical waves and waveguides. radiation and scattering.

New material (for me) in this course was limited to:

  • dispersion relations.
  • Druid-Lorentz model
  • quadropole moments
  • magnetic moments, magnetostatic force, and torque (mentioned in class without details, but studied from Jackson)
  • matrix representation of transmission and reflection through multiple interfaces

Antenna theory notes available on amazon

June 8, 2020 ece1229, math and physics play 2 comments , ,

I’ve received my copy of my bound Antenna Theory notes today:

I wanted a copy for myself, but don’t expect that anybody else would buy this particular notes compilation.  The course was taught from slides, and it was almost impossible to take good notes, so these aren’t much good without also having the (excellent) course text (Balanis.)

The two possible reasons to buy or download this notes compilation would be:

  • to peruse the solved problems, or
  • for the geometric algebra and tensor formalism exploration that followed from wondering how to deal with the magnetic sources that are used in this subject.

These notes are available for free in PDF form.  Should somebody other than me want to purchase their own copy on paper, it can be found on amazon for $8.50 USD.  I’ve set the price as close to amazon’s absolute minimum required price of $8.28, while also rounding up to a tidy multiple of $0.25

I find it curious that amazon requires a higher price (and royalty) just by virtue of enabling expanded distribution.  Since I wanted to buy my copy locally in the Canadian amazon marketplace ( to utilize my local prime shipping subscription, I had to set the price higher for all markets, including the US market (  Because shipping from the US to Canada is so high, it is cheaper for me to buy an aftermarket version using prime shipping from Canada, than to utilize kindle-direct-publishing’s option of buying an author draft (which would only be cost effective if I lived in the USA.)


EDIT: I misunderstood what Expanded Distribution (ED) meant.  This is to sell to markets that are outside of the 6 or so official amazon marketplaces (USA, Canada, UK, Germany, …, Japan).  I’ll probably take this book off of ED and lower the price instead.

Crashing Mathematica with HatchShading + Opacity

May 31, 2020 math and physics play No comments , , ,

I attempted to modify a plot for an electric field solution that I had in my old Antenna-Theory notes:
j \omega
\frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}
\lr{ 1 + \cos\theta }
-\cos\phi \thetacap
+ \sin\phi \phicap
and discovered that you can crash Mathematica ( by combining PlotStyle with Opacity and HatchShading (new in 12.1).  Here’s a stripped down version of the plot code that demonstrates the crash:

ClearAll[ rcap]
rcap = {Sin[#1] Cos[#2], Sin[#1] Sin[#2], Cos[#1]} & ;

rcap[t, p]
, {t, 0, π}
, {p, 0, 2 π}
, PlotStyle -> { HatchShading[0.5, Black]}
, ParametricPlot3D[
rcap[t, p]
, {t, 0, π}
, {p, 0, 2 π}
, PlotStyle -> {Directive[Opacity[0.5`]]}
], ParametricPlot3D[
,{p,0,2 π}
,PlotStyle\[Rule]{Directive[Opacity[0.5`]], HatchShading[0.5, \

The first two plots, using one, but not both of, Opacity or HatchShading work fine:

In this reproducer, the little dimple at the base has been removed, which was the reason for the Opacity.

I’ve reported the bug to Wolfram, but wonder if they are going to come back to me saying, “Well, don’t do that!”


EDIT: Fixed in Mathematica 12.1.1

My collection of Peeter Joot physics paperbacks

May 22, 2020 math and physics play No comments , , , , , , , ,

I ordered a copy of my old PHY456 Quantum Mechanics II notes for myself, and it arrived today!  Here it is with it’s buddies (Grad QM and QFT):

With the shipping cost from the US to Canada (because I’m now paying for amazon prime anyways) it’s actually cheaper for me to get a regular copy than to order an author proof, so this time I have no “not for resale” banding.

This little stack of Quantum notes weighs in at about 1050 pages, and makes a rather impressive pile.  There’s a lot of info there, for the bargain price of either free or about $30 USD, depending on whether you want a PDF or print copy of this set.  Of course, most people want neither, and get all their quantum mechanics through osmosis from the engineering of the microchips and electronics in their phones and computers.

I have to admit that it’s a fun ego boost to see your name in print.  In order to maximize the ego boost, you can use my strategy and do large scale vanity press, making a multiple volume set for yourself.  Here’s my whole collection, which includes the bulk of my course notes, plus my little book:

Based on the height of the stack, I’d guess this is about 3000 pages total, the product of about 10 years of study and work.

Making these all available for free to anybody in PDF form surely cripples my potential physical copy sales volume, but that doesn’t matter too much since I’ve set the price so low that I only get a token payment for each copy anyways.  Based on linear extrapolation of my sales so far, I’ll recoup my tuition costs (not counting the opportunity cost of working part time while I took the courses) after another 65 years of royalties.

My old Quantum II notes are now available on amazon

May 17, 2020 phy456 No comments , , , , , , , , ,

PHY456, Quantum Mechanics II was one of the first few courses that I did as part of my non-degree upper year physics program.  That was a self directed study part time program, where I took most of interesting seeming fourth year undergrad physics courses at UofT.

I was never really pleased with how my QMII notes came out, and unlike some of my other notes compilations, I never made a version available on amazon, instead just had the PDF available for free on my Quantum Mechanics page.  That page also outlines how to get a copy of the latex sources for the notes (for the curious, or for the zealous reader who wants to submit merge requests with corrections.)

Well, over the last month or so, I’ve gradually cleaned up these QMII notes enough that they are “print-ready” (no equations overflowing into the “gutter”, …) , and have gone ahead and made it available on amazon, for $10 USD.  Like my other class notes “books”, this is published using amazon’s print on demand service.  In the likely event that nobody will order a copy, there is no upfront requirement for me to order a minimal sized print run, and then be stuck with a whole bunch of copies that I can’t give away.

There are still lots of defects in this set of notes.  In particular, I seem to have never written up my problem set solutions in latex, and subsequently lost those solutions.  There’s also lots of redundant material, as I reworked a few of the derivations multiple times, and never went back and purged the crud.  That said, they are available as-is, now in paper form, as well as a free PDF.

I’ll share the preface, and the contents below.


These are my personal lecture notes for the Fall 2011, University of Toronto Quantum mechanics II course (PHY456H1F), taught by Prof. John E Sipe.

The official description of this course was:

“Quantum dynamics in Heisenberg and Schrodinger Pictures; WKB approximation; Variational Method; Time-Independent Perturbation Theory; Spin; Addition of Angular Momentum; Time-Dependent Perturbation Theory; Scattering.”

This document contains a few things

  • My lecture notes.
  • Notes from reading of the text \citep{desai2009quantum}. This may include observations, notes on what seem like errors, and some solved problems.
  • Different ways of tackling some of the assigned problems than the solution sets.
  • Some personal notes exploring details that were not clear to me from the lectures.
  • Some worked problems.

There were three main themes in this course, my notes for which can be found in

  • Approximate methods and perturbation,
  • Spin, angular momentum, and two particle systems, and
  • Scattering theory.

Unlike some of my other course notes compilations, this one is short and contains few worked problems. It appears that I did most of my problem sets on paper and subsequently lost my solutions. There are also some major defects in these notes:

  • There are plenty of places where things weren’t clear, and there are still comments to followup on those issues to understand them.
  • There is redundant content, from back to back lectures on materials that included review of the previous lecture notes.
  • A lot of the stuff in the appendix (mostly personal notes and musings) should be merged into the appropriate lecture note chapters. Some work along those lines has been started, but that work was very preliminary.
  • I reworked some ideas from the original lecture notes to make sense of them (in particular, adiabatic approximation theory), but then didn’t go back and consolidate all the different notes for the topic into a single coherent unit.
  • There were Mathematica notebooks for some of the topics with issues that I never did figure out.
  • Lots of typos, bad spelling, and horrendous grammar.
  • The indexing is very spotty.

Hopefully, despite these and other defects, these notes may be of some value to other students of Quantum Mechanics.

I’d like to thank Professor Sipe for teaching this course. I learned a lot and it provided a great foundation for additional study.

Phy456 (QM II) Contents:

  • Copyright
  • Document Version
  • Dedication
  • Preface
  • Contents
  • List of Figures
  • 1 Approximate methods.
  • 1.1 Approximate methods for finding energy eigenvalues and eigenkets.
  • 1.2 Variational principle.
  • 2 Perturbation methods.
  • 2.1 States and wave functions.
  • 2.2 Excited states.
  • 2.3 Problems.
  • 3 Time independent perturbation.
  • 3.1 Time independent perturbation.
  • 3.2 Issues concerning degeneracy.
  • 3.3 Examples.
  • 4 Time dependent perturbation.
  • 4.1 Review of dynamics.
  • 4.2 Interaction picture.
  • 4.3 Justifying the Taylor expansion above (not class notes).
  • 4.4 Recap: Interaction picture.
  • 4.5 Time dependent perturbation theory.
  • 4.6 Perturbation expansion.
  • 4.7 Time dependent perturbation.
  • 4.8 Sudden perturbations.
  • 4.9 Adiabatic perturbations.
  • 4.10 Adiabatic perturbation theory (cont.)
  • 4.11 Examples.
  • 5 Fermi’s golden rule.
  • 5.1 Recap. Where we got to on Fermi’s golden rule.
  • 5.2 Fermi’s Golden rule.
  • 5.3 Problems.
  • 6 WKB Method.
  • 6.1 WKB (Wentzel-Kramers-Brillouin) Method.
  • 6.2 Turning points..
  • 6.3 Examples.
  • 7 Composite systems.
  • 7.1 Hilbert Spaces.
  • 7.2 Operators.
  • 7.3 Generalizations.
  • 7.4 Recalling the Stern-Gerlach system from PHY354.
  • 8 Spin and Spinors.
  • 8.1 Generators.
  • 8.2 Generalizations.
  • 8.3 Multiple wavefunction spaces.
  • 9 Two state kets and Pauli matrices.
  • 9.1 Representation of kets.
  • 9.2 Representation of two state kets.
  • 9.3 Pauli spin matrices.
  • 10 Rotation operator in spin space.
  • 10.1 Formal Taylor series expansion.
  • 10.2 Spin dynamics.
  • 10.3 The hydrogen atom with spin.
  • 11 Two spins, angular momentum, and Clebsch-Gordon.
  • 11.1 Two spins.
  • 11.2 More on two spin systems.
  • 11.3 Recap: table of two spin angular momenta.
  • 11.4 Tensor operators.
  • 12 Rotations of operators and spherical tensors.
  • 12.1 Setup.
  • 12.2 Infinitesimal rotations.
  • 12.3 A problem.
  • 12.4 How do we extract these buried simplicities?
  • 12.5 Motivating spherical tensors.
  • 12.6 Spherical tensors (cont.)
  • 13 Scattering theory.
  • 13.1 Setup.
  • 13.2 1D QM scattering. No potential wave packet time evolution.
  • 13.3 A Gaussian wave packet.
  • 13.4 With a potential.
  • 13.5 Considering the time independent case temporarily.
  • 13.6 Recap.
  • 14 3D Scattering.
  • 14.1 Setup.
  • 14.2 Seeking a post scattering solution away from the potential.
  • 14.3 The radial equation and its solution.
  • 14.4 Limits of spherical Bessel and Neumann functions.
  • 14.5 Back to our problem.
  • 14.6 Scattering geometry and nomenclature.
  • 14.7 Appendix.
  • 14.8 Verifying the solution to the spherical Bessel equation.
  • 14.9 Scattering cross sections.
  • 15 Born approximation.
  • A Harmonic oscillator Review.
  • A.1 Problems.
  • B Simple entanglement example.
  • C Problem set 4, problem 2 notes.
  • D Adiabatic perturbation revisited.
  • E 2nd order adiabatically Hamiltonian.
  • F Degeneracy and diagonalization.
  • F.1 Motivation.
  • F.2 A four state Hamiltonian.
  • F.3 Generalizing slightly.
  • G Review of approximation results.
  • G.1 Motivation.
  • G.2 Variational method.
  • G.3 Time independent perturbation.
  • G.4 Degeneracy.
  • G.5 Interaction picture.
  • G.6 Time dependent perturbation.
  • G.7 Sudden perturbations.
  • G.8 Adiabatic perturbations.
  • G.9 WKB.
  • H Clebsh-Gordan zero coefficients.
  • H.1 Motivation.
  • H.2 Recap on notation.
  • H.3 The \(J_z\) action.
  • I One more adiabatic perturbation derivation.
  • I.1 Motivation.
  • I.2 Build up.
  • I.3 Adiabatic case.
  • I.4 Summary.
  • J Time dependent perturbation revisited.
  • K Second form of adiabatic approximation.
  • L Verifying the Helmholtz Green’s function.
  • M Mathematica notebooks.
  • Index
  • Bibliography

Exploring 0^0, x^x, and z^z.

May 10, 2020 math and physics play No comments , , , , , , ,

My Youtube home page knows that I’m geeky enough to watch math videos.  Today it suggested Eddie Woo’s video about \(0^0\).

Mr Woo, who has great enthusiasm, and must be an awesome teacher to have in person.  He reminds his class about the exponent laws, which allow for an interpretation that \(0^0\) would be equal to 1.  He points out that \(0^n = 0\) for any positive integer, which admits a second contradictory value for \( 0^0 \), if this was true for \(n=0\) too.

When reviewing the exponent laws Woo points out that the exponent law for subtraction \( a^{n-n} \) requires \(a\) to be non-zero.  Given that restriction, we really ought to have no expectation that \(0^{n-n} = 1\).

To attempt to determine a reasonable value for this question, resolving the two contradictory possibilities, neither of which we actually have any reason to assume are valid possibilities, he asks the class to perform a proof by calculator, computing a limit table for \( x \rightarrow 0+ \). I stopped at that point and tried it by myself, constructing such a table in Mathematica. Here is what I used

griddisp[labelc1_, labelc2_, f_, values_] := Grid[({
({{labelc1}, values}) // Flatten,
({ {labelc2}, f[#] & /@ values} ) // Flatten
}) // Transpose,
Frame -> All]
decimalFractions[n_] := ((10^(-#)) & /@ Range[n])
With[{m = 10}, griddisp[x, x^x, #^# &, N[decimalFractions[m], 10]]]
With[{m = 10}, griddisp[x, x^x, #^# &, -N[decimalFractions[m], 10]]]

Observe that I calculated the limits from both above and below. The results are

and for the negative limit

Sure enough, from both below and above, we see numerically that \(\lim_{\epsilon\rightarrow 0} \epsilon^\epsilon = 1\), as if the exponent law argument for \( 0^0 = 1 \) was actually valid.  We see that this limit appears to be valid despite the fact that \( x^x \) can be complex valued — that is ignoring the fact that a rigorous limit argument should be valid for any path neighbourhood of \( x = 0 \) and not just along two specific (real valued) paths.

Let’s get a better idea where the imaginary component of \((-x)^{-x}\) comes from.  To do so, consider \( f(z) = z^z \) for complex values of \( z \) where \( z = r e^{i \theta} \). The logarithm of such a beast is

\ln z^z
&= z \ln \lr{ r e^{i\theta} } \\
&= z \ln r + i \theta z \\
&= e^{i\theta} \ln r^r + i \theta z \\
&= \lr{ \cos\theta + i \sin\theta } \ln r^r + i r \theta \lr{ \cos\theta + i \sin\theta } \\
&= \cos\theta \ln r^r – r \theta \sin\theta
+ i r \lr{ \sin\theta \ln r + \theta \cos\theta },
z^z =
e^{ r \lr{ \cos\theta \ln r – \theta \sin\theta}} \times
e^{i r \lr{ \sin\theta \ln r + \theta \cos\theta }}.
In particular, picking the \( \theta = \pi \) branch, we have, for any \( x > 0 \)
(-x)^{-x} = e^{-x \ln x – i x \pi } = \frac{e^{ – i x \pi }}{x^x}.

Let’s get some visual appreciation for this interesting \(z^z\) beastie, first plotting it for real values of \(z\)

Plot[ {Re[x^x], Im[x^x]}, {x, -r, r}
, PlotRange -> {{-r, r}, {-r^r, r^r}}
, PlotLegends -> {Re[x^x], Im[x^x]}
], {{r, 2.25}, 0.0000001, 10}]

From this display, we see that the imaginary part of \( x^x \) is zero for integer values of \( x \).  That’s easy enough to verify explicitly: \( (-1)^{-1} = -1, (-2)^{-2} = 1/4, (-3)^{-3} = -1/27, \cdots \).

The newest version of Mathematica has a few nice new complex number visualization options.  Here’s two that I found illuminating, an absolute value plot that highlights the poles and zeros, also showing some of the phase action:

ComplexPlot[ x^x, {x, s (-1 – I), s (1 + I)},
PlotLegends -> Automatic, ColorFunction -> "GlobalAbs"], {{s, 4},
0.00001, 10}]

We see the branch cut nicely, the tendency to zero in the left half plane, as well as some of the phase periodicity in the regions that are in the intermediate regions between the zeros and the poles.  We can also plot just the phase, which shows its interesting periodic nature

ComplexPlot[ x^x, {x, s (-1 – I), s (1 + I)},
PlotLegends -> Automatic, ColorFunction -> "CyclicArg"], {{s, 6},
0.00001, 10}]

I’d like to take the time to play with some of the other ComplexPlot ColorFunction options, which appears to be a powerful and flexible visualization tool.

4800 pages of basic physics notes for $88 USD

September 29, 2019 math and physics play No comments , , , , , , , , , , , , , , , , , , , , , , , , , ,

Over the last 8 years I took most of the interesting 4th year undergraduate physics courses, and some graduate physics and engineering courses.

Well, my notes for much of that work are now available on (or .ca), or for free as PDF.  For the bargain price of $88, leveraging the time and money that I spent, you can get very comprehensive paperback notes for these subjects.  These notes aren’t textbook quality, but generally contain detailed expositions of the subjects and many worked problems.

Here’s what’s available:

Title Professor Year of study Format Price (USD) Pages
Quantum Mechanics I: Notes and problems for UofT PHY356 2010 Prof. Vatche Deyirmenjian Fall 2010 PDF $0.00 263
Quantum Mechanics II: Notes and problems for UofT PHY456 2011 Prof. John E. Sipe Fall 2011 PDF $0.00 320
Relativistic Electrodynamics: Notes and problems from 2011 PHY450H1S Prof. Erich Poppitz Winter  2011 Black and white $11.00 387
Classical Mechanics Prof. Erich Poppitz, + self-study Winter 2012 PDF $0.00 475
Advanced Classical Optics: Notes and problems from UofT PHY485H1F 2012 Prof. Joseph H. Thywissen Fall 2012 Black and white $11.00 382
Continuum Mechanics: Notes and problems from UofT PHY454H1S 2012 Prof. Kausik S. Das Winter 2012 Black and white $10.00 358
Basic Statistical Mechanics: Notes and problems from 2013 UofT PHY452H1S Prof. Arun Paramekanti Winter 2013 Black and white $11.00 399
Condensed Matter Physics: Notes and problems from UofT PHY487H1F 2013 Prof. Stephen Julian Fall 2013 Black and white $10.00 329
Modelling of Multiphysics Systems.  Notes and problems for UofT ECE1254 Prof. Piero Triverio Fall 2014 PDF $0.00 300
Graduate Quantum Mechanics: Notes and problems from 2015 UofT PHY1520H Prof. Arun Paramekanti Winter 2015 Black and white $12.00 435
Antenna Theory: Notes and problems for UofT ECE1229 Prof G. V. Eleftheriades Winter 2015 PDF $0.00 207
Electromagnetic Theory: Notes and problems for UofT ECE1228 Prof. M. Mojahedi Fall 2016 PDF $0.00 256
Geometric Algebra for Electrical Engineers: Multivector electromagnetism self-study 2016,2017 Colour $40.00 280
Geometric Algebra for Electrical Engineers: Multivector electromagnetism self-study 2016,2017 Black and white $12.00 280
Quantum Field Theory I: Notes and problems from UofT PHY2403 2018 Prof. Erich Poppitz Fall 2018 Black and white $11.00 423


That’s 4814 pages of notes for 0-$USD 88, depending on whether you want a PDF or paper copy (if available).  My cost per page is about $4.7 CAD, factoring in total tuition costs of ~$23000 CAD (most of which was for my M.Eng), but does not factor in the opportunity cost associated with the 20% paycut (w/ a switch to 80% hours) that I also took to find the time to fit in the study.

If you compare my cost of $4.7/page for these notes to FREE – $0.024/page, then I think you would agree that my offering is a pretty good deal!  While I have built in a $1 (+/- $0.50) royalty for the book formats, the chances of me recovering my costs are infinitesimal.

A few of the courses and/or collections of notes are not worth the effort of making print ready copies, and those notes are available only in PDF form.  An exception are my notes for Multiphyiscs Modelling, which was an excellent course, and I have excellent notes for, but I’ve been asked not to make those notes available for purchase in any form (even w/ $0 royalty.)


Continuum mechanics notes now in book format at

September 26, 2019 math and physics play No comments , , , , , ,

My notes from the 2012 UofT session of phy454, Continuum mechanics (aka fluid mechanics), are now available in book form on for $10 (black and white, softcover, 6×9″ format, 358 pages), as well as in PDF and latex formats as before.

I took that course as a non-degree student.  It was taught by Prof. Kausik S. Das, and had the official course description:

The theory of continuous matter, including solid and fluid mechanics. Topics include the continuum approximation, dimensional analysis, stress, strain, the Euler and Navier-Stokes equations, vorticity, waves, instabilities, convection and turbulence.

It was really only about fluid dynamics. Anything related to solids was really just to introduce the stress and strain tensors as lead up to expressing the Navier-Stokes equation. There was nothing in this course about beam deformation, Euler stability, or similar topics that one might have expected from the course description.

If you download the free PDF, compile the latex version, or buy a paper copy and feel undercharged, feel free to send some bitcoin my way.

Graduate Quantum Mechanics notes now available on paper from amazon

June 11, 2019 phy1520 No comments ,

My notes for “Graduate Quantum Mechanics” (PHY1520H) taught by Prof. Arun Paramekanti, fall 2015. (435 pages), are now available on paper (black and white) through kindle-direct-publishing for $12 USD.

This book is dedicated to my siblings.

Kindle-direct-publishing is a print on demand service, and allows me to make the notes available for pretty close to cost (in this case, about $6 printing cost, $5 to amazon, and about $1 to me as a token royalty).  The notes are still available for free in PDF form, and the latex sources are also available should somebody feel motivated enough to submit a merge request with corrections or enhancements.

This grad quantum course was especially fun.  When I took this class, I had enjoyed the chance to revisit the subject.  Of my three round match against QM, I came out much less bloody this time than the first two rounds.

These notes are no longer redacted and include whatever portions of the problem I completed, errors and all.  In the event that any of the problem sets are recycled for future iterations of the course, students who are taking the course (all mature grad students pursuing science for the love of it, not for grades) are expected to act responsibly, and produce their own solutions, within the constraints provided by the professor.


phy1520.V0.1.9-3 (June 10, 2019)

  • First version posted to kindle-direct successfully.
  • Lots of 6×9 formatting fixes made.
  • Add commas and periods to equations.
  • Remove blank lines that cause additional undesired indenting (implied latex \par’s).

Notes for Quantum Field Theory I (phy2403) now available in paper on amazon

May 2, 2019 phy2403 No comments , ,

My notes (423 pages, 6″x9″) from the fall 2018 session of the University of Toronto Quantum Field Theory I course (PHY2403), taught by Prof. Erich Poppitz, are now available on (through kindle-direct-publishing, formerly createspace).

These notes are available in three forms, two free, and one paper:

  • On amazon (kindle-direct-publishing) for $11 USD,
  • As a free PDF,
  • As latex sources (, makefiles, figures, …) to build/modify yourself.

This book is dedicated to dad.

Warning to students

These notes are no longer redacted and include whatever portions of the problem set 1-4 solutions I completed, errors and all.  In the event that any of the problem sets are recycled for future iterations of the course, students who are taking the course (all mature grad students pursuing science for the love of it, not for grades) are expected to act responsibly, and produce their own solutions, within the constraints provided by the professor.


The official course outline included:

  1. Introduction: Energy and distance scales; units and conventions. Uncertainty relations in the relativistic domain and the need for multiple particle description.
  2. Canonical quantization. Free scalar field theory.
  3. Symmetries and conservation laws.
  4. Interacting fields: Feynman diagrams and the S matrix; decay widths and phase space.
  5. Spin 1/2 fields: Spinor representations, Dirac and Weyl spinors, Dirac equation. Quantizing fermi fields and statistics.
  6. Vector fields and Quantum electrodynamics.