Physics

Path integral formulation

The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows a physicist to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these are coordinate space or Feynman path integrals), than the Hamiltonian. Possible downsides of the approach include that unitarity (this is related to conservation of probability; the probabilities of all physically possible outcomes must add up to one) of the S-matrix is obscure in the formulation. The path-integral approach has been proved to be equivalent to the other formalisms of quantum mechanics and quantum field theory. Thus, by deriving either approach from the other, problems associated with one or the other approach (as exemplified by Lorentz covariance or unitarity) go away.
The path integral also relates quantum and stochastic processes, and this provided the basis for the grand synthesis of the 1970s, which unified quantum field theory with the statistical field theory of a fluctuating field near a second-order phase transition. The Schrödinger equation is a diffusion equation with an imaginary diffusion constant, and the path integral is an analytic continuation of a method for summing up all possible random walks.
The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion. This idea was extended to the use of the Lagrangian in quantum mechanics by P. A. M. Dirac in his 1933 article. The complete method was developed in 1948 by Richard Feynman. Some preliminaries were worked out earlier in his doctoral work under the supervision of John Archibald Wheeler. The original motivation stemmed from the desire to obtain a quantum-mechanical formulation for the Wheeler–Feynman absorber theory using a Lagrangian (rather than a Hamiltonian) as a starting point.

 

https://en.wikipedia.org/wiki/Path_integral_formulation

Path integral formulation was last modified: July 27th, 2018 by Jovan Stosic

Hans Bethe

Hans Albrecht Bethe (German: [ˈhans ˈalbʁɛçt ˈbeːtə]; July 2, 1906 – March 6, 2005) was a German-American nuclear physicist who made important contributions to astrophysics, quantum electrodynamics and solid-state physics, and won the 1967 Nobel Prize in Physics for his work on the theory of stellar nucleosynthesis.[1][2]

For most of his career, Bethe was a professor at Cornell University.[3] During World War II, he was head of the Theoretical Division at the secret Los Alamos laboratory which developed the first atomic bombs. There he played a key role in calculating the critical mass of the weapons and developing the theory behind the implosion method used in both the Trinity test and the “Fat Man” weapon dropped on Nagasaki in August 1945.

After the war, Bethe also played an important role in the development of the hydrogen bomb, though he had originally joined the project with the hope of proving it could not be made. Bethe later campaigned with Albert Einstein and the Emergency Committee of Atomic Scientists against nuclear testing and the nuclear arms race. He helped persuade the Kennedy and Nixon administrations to sign, respectively, the 1963 Partial Nuclear Test Ban Treaty and 1972 Anti-Ballistic Missile Treaty (SALT I).

His scientific research never ceased and he was publishing papers well into his nineties, making him one of the few scientists to have published at least one major paper in his field during every decade of his career – which, in Bethe’s case, spanned nearly seventy years. Freeman Dyson, once one of his students, called him the “supreme problem-solver of the 20th century”.[4]

https://en.wikipedia.org/wiki/Hans_Bethe

Hans Bethe was last modified: July 15th, 2018 by Jovan Stosic

John Archibald Wheeler

John Archibald Wheeler (July 9, 1911 – April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission. Together with Gregory Breit, Wheeler developed the concept of the Breit–Wheeler process. He is best known for linking the term “black hole” to objects with gravitational collapse already predicted early in the 20th century, for coining the terms “quantum foam“, “neutron moderator“, “wormhole” and “it from bit“, and for hypothesizing the “one-electron universe“.

Wheeler earned his doctorate at Johns Hopkins University under the supervision of Karl Herzfeld, and studied under Breit and Bohr on a National Research Council fellowship. In 1939 he teamed up with Bohr to write a series of papers using the liquid drop model to explain the mechanism of fission. During World War II, he worked with the Manhattan Project‘s Metallurgical Laboratory in Chicago, where he helped design nuclear reactors, and then at the Hanford Site in Richland, Washington, where he helped DuPont build them. He returned to Princeton after the war ended, but returned to government service to help design and build the hydrogen bomb in the early 1950s.

For most of his career, Wheeler was a professor at Princeton University, which he joined in 1938, remaining until his retirement in 1976. At Princeton he supervised 46 PhDs, more than any other professor in the Princeton physics department.

https://en.wikipedia.org/wiki/John_Archibald_Wheeler

John Archibald Wheeler was last modified: July 15th, 2018 by Jovan Stosic

Julian Schwinger

Julian Seymour Schwinger (/ˈʃwɪŋər/; February 12, 1918 – July 16, 1994) was a Nobel Prize winning American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics (QED), in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order. Schwinger was a physics professor at several universities.

Julian Schwinger
Schwinger.jpg
Born Julian Seymour Schwinger
February 12, 1918
New York City, New York, U.S.
Died July 16, 1994(aged 76)
Los Angeles, California, U.S.
Nationality United States
Alma mater City College of New York
Columbia University
Known for Quantum electrodynamics
Spin–statistics theorem
Sigma model
MacMahon Master theorem
List of things named after Julian Schwinger
Spouse(s) Clarice Carrol (m. 1947)
Awards Albert Einstein Award(1951)
National Medal of Science (1964)
Nobel Prize in Physics (1965)
Scientific career
Fields Physics
Institutions University of California, Berkeley
Purdue University
Massachusetts Institute of Technology
Harvard University
University of California, Los Angeles
Doctoral advisor Isidor Isaac Rabi
Doctoral students Roy Glauber
Ben R. Mottelson
Sheldon Lee Glashow
Walter Kohn
Bryce DeWitt
Daniel Kleitman
Sam Edwards
Gordon Baym
Lowell S. Brown
Stanley Deser
Lawrence Paul Horwitz
Margaret G. Kivelson
Tung-Mow Yan

Julian Schwinger, winner of the 1965 Nobel Prize in Physics. Original caption: “His laboratory is his ballpoint pen.”

Schwinger is recognized as one of the greatest physicists of the twentieth century, responsible for much of modern quantum field theory, including a variational approach, and the equations of motion for quantum fields. He developed the first electroweakmodel, and the first example of confinement in 1+1 dimensions. He is responsible for the theory of multiple neutrinos, Schwinger terms, and the theory of the spin 3/2 field.

https://en.wikipedia.org/wiki/Julian_Schwinger

Julian Schwinger was last modified: July 15th, 2018 by Jovan Stosic

Fifth force

In physics, the fifth force is a proposed fundamental force, additional to the four known fundamental forces of nature. The conventionally accepted fundamental forces that form the basis of all known interactions are the gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative theories have proposed a fifth force to explain various anomalous observations that do not fit existing theories; the characteristics of this fifth force depend on the theory being advanced. Many postulate a force roughly the strength of gravity(i.e. it is much weaker than electromagnetism or the nuclear forces) with a range of anywhere from less than a millimeter to cosmological scales. Another proposal is a new weak force, mediated by W’ and Z’ bosons.

The search for a fifth force has increased in recent decades due to the discovery that most of the mass of the universe is accounted for by an unknown form of matter called dark matter. Most physicists believe that dark matter is some new undiscovered subatomic particle, but some believe that it could be related to an unknown fundamental force. It has also recently been discovered that the expansion of the universe is accelerating, which has been attributed to a form of energy called dark energy, and some physicists speculate that a form of dark energy called quintessence could be the fifth force.[1][2][3

https://en.wikipedia.org/wiki/Fifth_force

Fifth force was last modified: July 14th, 2018 by Jovan Stosic

Freeman Dyson

Freeman John Dyson FRS (born 15 December 1923) is an English-born American theoreticalphysicist and mathematician, known for his work in quantum electrodynamicssolid-state physicsastronomy and nuclear engineering.[7][8] He is professor emeritus at the Institute for Advanced Study, a Visitor of Ralston College,[9] and a member of the Board of Sponsors of theBulletin of the Atomic Scientists.[10]
https://en.m.wikipedia.org/wiki/Freeman_Dyson

Freeman Dyson was last modified: November 13th, 2017 by Jovan Stosic

Marcel Grossmann

Marcel Grossmann (HungarianGrossmann Marcell, April 9, 1878 – September 7, 1936) was a mathematician and a friend and classmate of Albert Einstein. Grossmann was a member of an old Swiss family from Zurich. His father managed a textile factory. He became a Professor of Mathematics at the Federal Polytechnic School in Zurich, today the ETH Zurich, specializing in descriptive geometry.
https://en.m.wikipedia.org/wiki/Marcel_Grossmann

Marcel Grossmann was last modified: September 25th, 2017 by Jovan Stosic