International Journal of Modern Physics A

Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.

As all of those present who knew my father will remember that he was a very shy man and he always avoided interviews with the press. He refused to talk to reporters and avoided having his photograph taken when ever possible. I think that this is probably why so many published accounts of his life failed to capture his personal side, especially one published in the last decade by the Scientific American. For this reason, I am happy to have the opportunity to share with you some of my memories of him, and to try and put the record straight.

The Dirac equation explained why the gyromagnetic ratio, g factor, is equal to 2 for fundamental spin particles. Quantum loop effects were subsequently shown to induce a small shift or anomaly, a≡(g-2)/2. Anomalous magnetic moment effects have been calculated and measured with extraordinary precision for the electron and muon. Here, the Standard Model's predictions for a_l=(g_l-2)/2, l=e, μ are described and compared with experimental values. Implications for probing "New Physics" effects are also discussed.

One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N=4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset F₄/SO(9). The divergences are proportional to the trace over a non-compact structure containing the compact form of F₄. Its nature is still unknown, but it could show the way to M-theory.

I provide a very brief sketch of Dirac's Hamiltonian formulation of Einstein's theory, in its relation both to his own earlier work and to contemporary developments.

The relevance of the Dirac equation for computations of nuclear structure is motivated and discussed. Quantitatively successful results for medium- and heavy-mass nuclei are described, and modern ideas of effective field theory and density functional theory are used to justify them.

Dirac's quantization of magnetic monopole strength is derived without reference to a (singular, patched) vector potential.

Dirac showed that the existence of magnetic monopoles would imply quantization of electric charge. I discuss the converse, and propose two 'principles of completeness' which I illustrate with various examples. Presented at the Dirac Centennial Symposium, Tallahassee, Dec. 6-7, 2002.

Time variation of fundamental constants would not be surprising in the framework of theories involving extra dimensions. The variation of any one constant is likely to be correlated with variations of others in a pattern that is diagnostic of the underlying physics.

Some of my earlier arguments, suggesting modifications of the Standard Model of Particle Physics (see ref. ¹), are elaborated and extended. Rules deduced from the known properties of elementary fermions are sharpened and extended in the first part. Conclusions drawn from the rules in the second part are also honed and expanded and an estimate of the neutrino mass eigenstates is added. In the third part, a tentative explanation of the rules is discussed. In my earlier paper, I suggested replacing the point-sources postulated by the Standard Model for each generation by finite 'source-shapes', equal for all elementary fermions of a generation and systematically decreasing in volume from the first to the third generation, thus increasing the effect of self-interactions. According to the rules a correlation exists between the mass of an elementary fermion and the strength of its self-interaction, thus an increase in self-interactions would resolve the problem of the hierarchical masses. A possible connection between the existence of only three generations and the three-dimensionality of space also is discussed. In the epilogue the question is explored whether finite source-shapes for the elementary fermions can be reconciled with fundamental theoretical tenets.