Civil Rights
Movements, leaders, victories and the continuing fight for equality.
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THE BHP WIRE —
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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
Innovation, patents, science, technology and world-changing contributions.
Pioneers, champions, Negro Leagues, records, activism and excellence.
Meet the people whose lives, choices and achievements shaped the journey.
Black towns, communities, institutions and places where history happened.
Moments that changed communities, movements, institutions and the nation.
Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
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| Fundamental objects |
| Perturbative theory |
| Non-perturbative results |
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Green–Schwarz (GS) formalism (named after Michael Green and John H. Schwarz)[1][2][3] is an attempt to introduce fermions in string theory. The theory is equivalent to RNS formalism which has been GSO projected. This theory is very hard to quantize, being straightforward to quantize only in light cone gauge.[4] A covariant quantization of spinning string, maintaining space-time supersymmetry manifest, is possible in a formalism inspired on the GS formalism, known as pure spinor formalism.[5]
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Green–Schwarz (GS) formalism (named after Michael Green and John H. Schwarz) is an attempt to introduce fermions in string theory. The theory is equivalent to RNS formalism which has been GSO projected. This theory is very hard to quantize, being straightforward to quantize only in light cone gauge. A covariant quantization of spinning string, maintaining space-time supersymmetry manifest, is possible in a formalism inspired on the GS formalism, known as pure spinor formalism.
In string theory, the Ramond–Neveu–Schwarz (RNS) formalism is an approach to formulating superstrings in which the worldsheet has explicit superconformal invariance but spacetime supersymmetry is hidden, in contrast to the Green–Schwarz formalism where the latter is explicit. It was originally developed by Pierre Ramond, André Neveu and John Schwarz in the RNS model in 1971, which gives rise to type II string theories and can also give type I string theory. Heterotic string theories can also be acquired through this formalism by using a different worldsheet action. There are various ways to quantize the string within this framework including light-cone quantization, old canonical quantization, and BRST quantization. A consistent string theory is only acquired if the spectrum of states is restricted through a procedure known as a GSO projection, with this projection being automatically present in the Green–Schwarz formalism.
The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region – such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft in 1993, it was given a precise string theoretic interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Susskind said, "The three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description from which gravity emerges in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence. The holographic principle was inspired by the Bekenstein bound of black hole thermodynamics, which conjectures that the maximum entropy in any region scales with the radius squared, rather than cubed as might be expected. In the case of a black hole, the insight was that the information content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory. However, there exist classical solutions to the Einstein equations that allow values of the entropy larger than those allowed by an area law (radius squared), hence in principle larger than those of a black hole. These are the so-called "Wheeler's bags of gold". The existence of such solutions conflicts with the holographic interpretation, and their effects in a quantum theory of gravity including the holographic principle are not yet fully understood.
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. It is a quantum of gravitational wave energy. There is no complete quantum field theory of gravitons due to the unsolved mathematical problem of renormalization in general relativity. This problem is avoided in string theory, which has the graviton as a massless state of a fundamental string, but that theory has not made sufficient progress. If it exists, the graviton is expected to be massless because the gravitational force has a very long range and appears to propagate at the speed of light. The graviton must be a spin-2 boson because the source of gravitation is the stress–energy tensor, a second-order tensor (compared with electromagnetism's spin-1 photon, the source of which is the four-current, a first-order tensor). Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way gravitational interactions do. This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Shirley Chisholm, elected in 1968.