John Henry Schwarz

"Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,R)/SO(2)."

"The second superstring revolution (1994-??) has brought non-perturbative string physics within reach. The key discoveries were the recognition of amazing and surprising "dualities." They have taught us that what we viewed previously as five theories is in fact five different perturbative expansions of a single underlying theory about five different points! It is now clear that there is a unique theory, though it may allow many different vacua. ... Three different kinds of dualities, called S, T, and U have been identified.""

"As I once told a newspaper reporter, in order to be sure to be quoted: discovery of supersymmetry would be more profound than life on Mars."

"String theory is an ambitious approach to the construction of a mathematical description of the physics that governs the properties of elementary particls and their interactions as well as the structure of space and time. It incorporates (and maybe even explains) well-established principles such as quantum mechanics and relativity. In fact, many string theorists (myself included) believe that string theory constitutes the third big physics revolution of the century, following relativity and quantum mechanics. It certainly requires conceptual advances every bit as bizarre and unexpected as was the case in the prior two revolutions."

"In the early 1960s there existed a successful quantum theory of the electromagnetic force (QED), which was completed in the late 1940s, but the theories of the weak and strong nuclear forces were not yet known. In UC Berkeley, where I was a graduate student during the period 1962 – 66, the emphasis was on developing a theory of the strong nuclear force. I felt that UC Berkeley was the center of the Universe for high energy theory at the time. Geoffrey Chew (my thesis advisor) and Stanley Mandelstam were highly influential leaders. Also, Steve Weinberg and Shelly Glashow were impressive younger faculty members. David Gross was a contemporaneous Chew student with whom I shared an office."

"Among the problems of the known string theories, as a theory of hadrons, was the fact that the spectrum of open strings contains massless spin 1 particles, and the spectrum of closed strings contains a massless spin 2 particle (as well as other massless particles), but there are no massless hadrons. In 1974, Joël Scherk and I decided to take string theory seriously as it stood, rather than forcing it to conform to our preconceptions. ... Specifically, Scherk and Schwarz (1974) proposed trying to interpret string theory as a unified quantum theory of all forces including gravity. Neveu and Scherk (1972) had shown that string theory incorporates the correct gauge invariances to ensure agreement at low energies (compared to the scale given by the string tension) with Yang-Mills theory. Yoneya (1973,1974) and Scherk and Schwarz (1974) showed that it also contains gauge invariances that ensure agreement at low energies with general relativity."

"One of the facts of nature is that there is what's called parity violation, which means that the fundamental laws are not invariant under mirror reflection. For example, a neutrino always spins clockwise and not counterclockwise, so it would look wrong viewed in a mirror. When you try to write down a fundamental theory with parity violation, mathematical inconsistencies often arise when you take account of quantum effects. This is referred to as the anomaly problem. It appeared that one couldn't make a theory based on strings without encountering these anomalies, which, if that were the case, would mean strings couldn't give a realistic theory. Green and I discovered that these anomalies cancel one another in very special situations. When we released our results in 1984, the field exploded. That's when Edward Witten [a theoretical physicist at the Institute for Advanced Study in Princeton], probably the most influential theoretical physicist in the world, got interested. Witten and three collaborators wrote a paper early in 1985 making a particular proposal for what to do with the six extra dimensions, the ones other than the four for space and time. That proposal looked, at the time, as if it could give a theory that is quite realistic. These developments, together with the discovery of another version of superstring theory, constituted the first superstring revolution."

"While spectacularly successful at predicting the behavior of atoms and subatomic particles, the quantum laws looked askance at Einstein's formulation of gravity. This set the stage for more than a half-century of despair as physicists valiantly struggled, but repeatedly failed, to meld general relativity and quantum mechanics, the laws of the large and small, into a single all-encompassing description. Such was the case until December 1984, when John Schwarz, of the California Institute of Technology, and Michael Green, then at Queen Mary College, published a once-in-a-generation paper showing that string theory could overcome the mathematical antagonism between general relativity and quantum mechanics, clearing a path that seemed destined to reach the unified theory."