Steven Weinberg, ‘The Langragian of the Electroweak Theory’, 2014, Bernard Jacobson Gallery

A portfolio of aquatints, 22 x 30, hand drawn by notable mathematicians and physicists of equations/expressions/formulas associated with their work. Curated and with an introductory text by Daniel Rockmore, Professor of Mathematics and Computer Science, Dartmouth College. Each of the prints is accompanied with a letterpress text by the contributor as well as a hand signed certificate of authenticity.
This equation present the original version of what has become the standard theory of two fundamental forces of nature, the electromagnetism, is responsible for an important kind of radioactivity, known as beta decay, and for the first step in the chain of nuclear reactions that gives heat to the sun and stars. This equation was Eq. (4) in my first paper in this subject, published in 1967. This was for some years the most widely cited paper ever published in elementary particle physics, and may still be. The electroweak theory is a filed theory. Its fundamental ingredients are fields, including the electric and magnetic field. The quantity denoted by £ on the left hand side of the equation is a combonation of fields and their rates of change, known as the Lagrangian density of this theory. The Lagrangian density is something like an energy density, and it provides a convenient way of summarizing all the equations governing the fields of the theory, following rules that have been used by physicist since 1930s. Most of the symbols on the right- hand side of the equation denote the various fields of the theory. The weak and electromagnetic forces are transmitted by the fields Au and Bu; the electric and magnetic fields are combinations of Au and Bu. The neutrino and the left-handed part of the electron field(thatis, the field that describes electrons that are spinning around their directions of motion like the fingers of the left hand curling around the thumb) are united in symbol L; the right-handed part of the electron field is denoted R. The quantities g and g' are numerical constants, related to the charge of the electron, whose values have to be taken from the experiment.
The thirs and fourth lines of the equation describe the mechanism by which the symmetry of the theory between neutrinos and left-handed electrons, and between the weak and eletromagnetic forces, is broken. The symbol () denotes a quarter of fields, whose interaction with the other fields gives mass to the electron, leaving the neutrino massless, and gives mass to the three particles that transmit the weak forces, leaving the photon (the particle of light) massless. The quantities Ge' M1 2 and h are additional numerical constants, related to the mass of the electron and the strength of the weak forces. One of the quartet of fields included in () corresponds to a new particle, which was not discovered experimentally until 2012. This equation may not look beautiful. Its beauty lies in its rigidity - once its ingredits are specified, its structure is pretty well fixed by conditions of mathematical consistency. Leave out one line, or just change a minus sign to a plus sign and the whole thing would become inconsistent. For brevity, this equation left out the muon, a heavier electron-like particle, and a corresponding type of neutrino. It was obvious that they should be included the same way as the electron and its neutrino. In 1971 the theory was expanded to include quarks, the elementary particles that make up the protons and neutrons. Since then the theory has been repeatedly confirmed by experiment.

Publisher: Co-Published by Yale University Art Gallery, New Haven, CT. and Parasol Press, Ltd., Portland, OR in association with Bernard Jacobson Gallery, London, England.

About Steven Weinberg