This book takes the reader from some elementary ideas about groups to the essence of the Standard Model of particle physics along a relatively straight and intuitive path. Groups alone are first used to arrive at a classical analog  of the Dirac equation. Using elementary quantum mechanics, this analog can be turned into the actual Dirac equation, which governs the motion of the quarks and leptons of the Standard Model. After introduction to the gauge principle, the groups introduced in the beginning of the book are used to give an introduction to the Standard Model. The idea is to give an Olympian view of this evolution, one that is often missing when absorbing the detailed subject matter of the Standard Model as presented in an historical approach to the subject.

Published by World Scientific:

Errata: p. 110, Eq. (A3.3), a right parenthesis is missing after the 1st derivative in the second line of the equation and the exponent “v” in both lines of the equation should be changed to the Greek “nu”; p. 117 has a duplicated paragraph.  Appendix A, p.87, 1st paragraph, line 2:   2.7 X 10^-22 should be 4 X 10^-20.

NYT: “A Nuclear Legacy Within Reach”

The 8 August 2016 lead editorial of the New York Times made a financial argument against modernization of the nuclear arsenal — including the land-based intercontinental ballistic missiles.  They then noted that former Defense Secretary William Perry had argued that land-based intercontinental ballistic missiles are no longer needed.  Concluding that, “the time has come to think seriously about whether that leg of the traditional air-sea-land triad should be gradually retired”.   Only one letter was published on 15 August that partly addressed the real problem associated with this leg of the triad.  Here is the letter I wrote that addresses the issue:

To the Editor:

William Perry, as you report in your editorial of 8 August, is correct that land-based intercontinental ballistic missiles are no longer needed. What was not said is that their mere existence increases the probability of accidental war.  As former defense secretary Perry well knows, these missiles are not survivable under nuclear attack.  Historically, and no doubt currently, the lack of survivability drives national policy to a launch-on-warning posture.  What this means is that when satellite and radar systems both indicate a massive ballistic missile attack, the President is given barely enough time to make a couple of phone calls before he must make the decision to launch the missiles or lose them.  It has happened in the past that both satellite and radar systems have falsely indicated a nuclear attack.  The nation went to the highest defense readiness condition but luckily the indication of an attack was found to be a false alert before the President was called.

At one time land-based ballistic missiles had a greater accuracy than survivable sea-based systems, but this hasn’t been the case for many years.  The country would be well served by taking this opportunity to unilaterally eliminate them.


The chiral anomaly is a purely quantum mechanical phenomenon that has a long history dating back to the late 1960s. Surprisingly, it has recently made a macroscopic appearance in condensed matter physics. A brief introduction to the relevant features of this anomaly is given and it is shown that its appearance in condensed matter systems must involve force-free magnetic fields, which may help explain the long current relaxation times in Dirac and Weyl semimetals.

Canadian Journal of Physics: Published on the web 13 March 2017, 10.1139/cjp

The published version is available here:



The late 19th and 20th centuries brought a revolution in the scientific understanding of the universe around us, one whose effects are still being felt around the world as it forces people to change their conception of the universe and the place of human beings within it.  Perhaps the greatest remaining mystery is the nature of consciousness itself, which has been a subject of human inquiry for at least the last several millennia. In this essay, I discuss the nature of thought and consciousness and argue that that consciousness and thought are natural biological phenomena.

Updated version (4 April 2016)



The idea that particles are the basic constituents of all matter dates back to ancient times and formed the basis of physical thought well into modern times. The debate about whether light was a wave or a stream of particles also lasted until relatively recently. It was the advent of de Broglie’s work and its implications that revolutionized the concept of an elementary particle–but unfortunately did not banish the idea of a point particle despite its difficulties in both classical and quantum physics. Some of these problems are discussed in this essay, which covers chiral oscillations, Penrose’s “zigzag” picture of particles satisfying the Dirac equation, and some ideas derived from string theory.



(with S. Fred Singer)

Many people believe that wind and solar energy are essential for replacing nonrenewable fossil fuels. They also believe that wind and solar are unique in providing energy that’s carbon-free and inexhaustible. A closer look shows that such beliefs are based on illusions and wishful thinking.

Op-Ed in The Bridge: Linking Engineering and Society (Winter 2015)

Published quarterly by the National Academy of Engineering



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