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" "Electromagnetism becomes stronger as we go to higher energies, or equivalently shorter distances.
Physically, the origin of this phenomenon is closely related to the physics of dielectrics. Consider a photon interacting with an electron, which we will call the test electron to avoid confusion in what follows. Due to quantum fluctuations ... , spacetime is full of electron-positron pairs, popping in and out of existence. Near the test electron, the electrons in these virtual pairs are repelled by the test electron and thus tend to move away from the test electron while the positrons tend to move toward the test electron. Thus, at long distances, the charge of the test electron is shielded to some extent by the cloud of positrons, causing a weaker coupling to the photon, while at short distances the coupling to the photon becomes stronger. The quantum vacuum is just as much a dielectric as a lump of actual material.
Anthony Zee (, b. 1945) (Zee comes from the Shanghainese pronunciation of 徐) is a Chinese-American physicist and author.
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We discuss the problem of adding random matrices, which enable us to study Hamiltonians consisting of a deterministic term plus a random term. Using a diagrammatic approach and introducing the concept of "gluon connectedness," we calculate the density of energy levels for a wide class of probability distributions governing the random term, thus generalizing a result obtained recently by Brézin, Hikami, and Zee. The method used here may be applied to a broad class of problems involving random matrices.
In a course on nonrelativistic quantum mechanics you learned about the Pauli exclusion principle2 and its later generalization stating that particles with half integer spins, such as electrons, obey Fermi-Dirac statistics and want to stay apart, while in contrast particles with integer spins, such as photons or pairs of electrons, obey Bose-Einstein statistics and love to stick together. From the microscopic structure of atoms to the macroscopic structure of neutron stars, a dazzling wealth of physical phenomena would be incomprehensible without this spin-statistics rule. Many elements of condensed matter physics, for instance, band structure, Fermi liquid theory, superfluidity, superconductivity, quantum Hall effect, and so on and so forth, are consequences of this rule.
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Although group theory is certainly relevant for nineteenth-century physics, it really started to play an important role with the work of Lorentz and Poincaré, and became essential with quantum mechanics. Heisenberg opened up an entirely new world with his vision of an internal symmetry, the exploration of which continues to this day in one form or another. Beginning in the 1950s, group theory has come to play a central role in several areas of physics, perhaps none more so than in what I call fundamental physics ...