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Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and in particle physics, for which he proposed the parton model. For his contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga. Feynman developed a pictorial representation scheme for the mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams and is widely used. During his lifetime, Feynman became one of the best-known scientists in the world. In a 1999 poll of 130 leading physicists worldwide by the British journal ''Physics World'', he was ranked the seventh-greatest physicist of all time. He assisted in the Manhatt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mountain View Cemetery, Altadena
Mountain View Cemetery and Mausoleum is a historic cemetery in Altadena, California, Altadena, California, United States. Established in 1882, it contains over 70,000 burials in its approximately , including Pasadena's pioneering families and California statesmen and women. It also contains a section for American Civil War, Civil War burials. The cemetery also includes a mausoleum, located across the street on Marengo Avenue, and the Pasadena Mausoleum, on Raymond Avenue.About us - Mountain View's official website History In the frontier era, the residents of Pasadena buried their relatives on family property. Colonel Jabez Banbury's son, Charles, for example, was buried on land that occupied part of the Arroyo Seco, now part of the Wrigley Estate. Banbury sold his property in 1882, at which point Levi W. Giddings set aside part of h ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul J
Paul may refer to: People * Paul (given name), a given name, including a list of people * Paul (surname), a list of people * Paul the Apostle, an apostle who wrote many of the books of the New Testament * Ray Hildebrand, half of the singing duo Paul & Paula * Paul Stookey, one-third of the folk music trio Peter, Paul and Mary * Billy Paul, stage name of American soul singer Paul Williams (1934–2016) * Vinnie Paul, drummer for American Metal band Pantera * Paul Avril, pseudonym of Édouard-Henri Avril (1849–1928), French painter and commercial artist * Paul, pen name under which Walter Scott wrote ''Paul's letters to his Kinsfolk'' in 1816 * Jean Paul, pen name of Johann Paul Friedrich Richter (1763–1825), German Romantic writer Places * Paul, Cornwall, a village in the civil parish of Penzance, United Kingdom * Paul (civil parish), Cornwall, United Kingdom * Paul, Alabama, United States, an unincorporated community * Paul, Idaho, United States, a city * Paul, Nebraska ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Sprinkler
A Feynman sprinkler, also referred to as a Feynman inverse sprinkler or reverse sprinkler, is a sprinkler-like device which is submerged in a tank and made to suck in the surrounding fluid. The question of how such a device would turn was the subject of an intense and remarkably long-lived debate. The device generally remains steady with no rotation, though with sufficiently low friction and high rate of inflow, it has been seen to turn weakly in the opposite direction of a conventional sprinkler. A regular sprinkler has nozzles arranged at angles on a freely rotating wheel such that when water is pumped out of them, the resulting jets cause the wheel to rotate; a Catherine wheel and the aeolipile ("Hero's engine") work on the same principle. A "reverse" or "inverse" sprinkler would operate by aspirating the surrounding fluid instead. The problem is commonly associated with theoretical physicist Richard Feynman, who mentions it in his bestselling memoirs '' Surely You're Joking, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Slash Notation
In the study of Dirac fields in quantum field theory, Richard Feynman introduced the convenient Feynman slash notation (less commonly known as the Dirac slash notation). If ''A'' is a covariant vector (i.e., a 1-form), : \ \stackrel\ \gamma^0 A_0 + \gamma^1 A_1 + \gamma^2 A_2 + \gamma^3 A_3 where ''γ'' are the gamma matrices. Using the Einstein summation notation, the expression is simply : \ \stackrel\ \gamma^\mu A_\mu. Identities Using the anticommutators of the gamma matrices, one can show that for any a_\mu and b_\mu, :\begin = a^\mu a_\mu \cdot I_4 = a^2 \cdot I_4 \\ + = 2 a \cdot b \cdot I_4. \end where I_4 is the identity matrix in four dimensions. In particular, :^2 = \partial^2 \cdot I_4. Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example, :\begin \gamma_\mu \gamma^\mu &= -2 \\ \gamma_\mu \gamma^\mu &= 4 a \cdot b \cdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram. Propagators may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called ''(causal) Green's functions'' (called "''causal''" to distinguish it from the elliptic Laplacian Green's function). Non-relativistic propagators In non-relativistic quantum mechanics, the propagator gives the probability amplitude for a particle to travel from one spatial point (x') at one time (t') to another spatial point (x) at a later time (t). The Green's function G for the Schrödinger equation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Point
A sequence of six consecutive nines occurs in the decimal representation of the number pi (), starting at the 762nd decimal place.. It has become famous because of the mathematical coincidence, and because of the idea that one could memorize the digits of up to that point, and then suggest that is rational. The earliest known mention of this idea occurs in Douglas Hofstadter's 1985 book '' Metamagical Themas'', where Hofstadter states This sequence of six nines is colloquially known as the "Feynman point", after physicist Richard Feynman, who allegedly stated this same idea in a lecture.. However it is not clear when, or even if, Feynman ever made such a statement. It is not mentioned in his memoirs and unknown to his biographer James Gleick. Related statistics is conjectured, but not known, to be a normal number. For a normal number sampled uniformly at random, the probability of a specific sequence of six digits occurring this early in the decimal representation is about ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Parametrization
Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well. It was introduced by Julian Schwinger and Richard Feynman in 1949 to perform calculations in quantum electrodynamics. Formulas Richard Feynman observed that :\frac=\int^1_0 \frac which is valid for any complex numbers ''A'' and ''B'' as long as 0 is not contained in the line segment connecting ''A'' and ''B.'' The formula helps to evaluate integrals like: :\begin \int \frac &= \int dp \int^1_0 \frac \\ &= \int^1_0 du \int \frac. \end If ''A''(''p'') and ''B''(''p'') are linear functions of ''p'', then the last integral can be evaluated using substitution. More generally, using the Dirac delta function \delta: :\begin \frac&= (n-1)! \int^1_0 du_1 \cdots \int^1_0 du_n \frac \\ &=(n-1)! \int^1_0 du_1 \int^_0 du_2 \cdots \int^_0 du_ \frac. \end This formula is valid fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman–Kac Formula
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes. In 1947, when Kac and Feynman were both faculty members at Cornell University, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. The Feynman–Kac formula resulted, which proves rigorously the real-valued case of Feynman's path integrals. The complex case, which occurs when a particle's spin is included, is still an open question. It offers a method of solving certain partial differential equations by simulating random paths of a stochastic process. Conversely, an important class of expectations of random processes can be computed by deterministic methods. Theorem Consider the partial differential equation \fracu(x,t) + \mu(x,t) \fracu(x,t) + \tfrac \sigma^2(x,t) \fracu(x,t) -V(x,t) u(x,t) + f(x,t) = 0, defined for all x \in \mathbb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Gauge
In the physics of gauge theory, gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant Degrees of freedom (physics and chemistry), degrees of freedom in field (physics), field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a certain transformation, equivalent to a symmetry transformation, shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom. Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The calculation of probability amplitudes in theoretical particle physics requires the use of large, complicated integrals over a large number of variables. Feynman diagrams instead represent these integrals graphically. Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams apply primarily to quantum field theory, they can be used in other areas of physics, such as solid-state theory. Frank Wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Checkerboard
The Feynman checkerboard, or relativistic chessboard model, was Richard Feynman's sum-over-paths formulation of the kernel for a free spin- particle moving in one spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums. The model can be visualised by considering relativistic random walks on a two-dimensional spacetime checkerboard. At each discrete timestep \epsilon the particle of mass m moves a distance \epsilon c to the left or right (c being the speed of light). For such a discrete motion, the Feynman path integral reduces to a sum over the possible paths. Feynman demonstrated that if each "turn" (change of moving from left to right or conversely) of the space–time path is weighted by -i \epsilon mc^2/\hbar (with \hbar denoting the reduced Planck constant), in the limit of infinitely small checkerboard squares the sum of all weighted paths yields a propagator that satisfies the one-dimensional Dira ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
