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	PlanetMath: Feynman path integral
		The argument is by analogy to the Gaussian integral
		The Feynman path integral was constructed as part of a re-formulation of quantum field theory by Richard Feynman, based on the sum-over-histories postulate of quantum mechanics, and can be thought of as an adaptation of Green's function methods for solving initial/boundary value problems.
		This is version 15 of Feynman path integral, born on 2002-05-31, modified 2007-06-17.
	planetmath.org /encyclopedia/FeynmannPathIntegral.html (268 words)

	Long Now: Views: Essays
		Feynman decided to test this assumption on a problem that he was familiar with in detail: quantum chromodynamics.
		Feynman's router equations were in terms of variables representing continuous quantities such as "the average number of 1 bits in a message address." I was much more accustomed to seeing analysis in terms of inductive proof and case analysis than taking the derivative of "the number of 1's" with respect to time.
		Feynman was always quick to point out to them that he considered their specific models "kooky," but like the Connection Machine, he considered the subject sufficiently crazy to put some energy into.
	www.longnow.org /views/essays/articles/ArtFeynman.php (4333 words)

	Physics Today August 2001
		It was clear to Feynman that his "path integral" was no integral in the ordinary sense of the word, and that what he called its "summation over histories" did not involve a measure in the usual sense.
		It was invented by Feynman in 1951 in an attempt to "disentangle" exponentials of noncommuting operators such as often occur in time-ordered perturbation theory (commonly known as the Dyson time-ordered exponential).
		Feynman realized that his highly heuristic approach poses serious mathematical problems, and this book appears to be a first systematic, mathematically rigorous study of this subject.
	physicstoday.org /pt/vol-54/iss-8/p48.html (833 words)

	» Bookshelf « e pur si muove - recherche en dépaysement
		Path integrals are an example of high-powered math that rarely shows up in undergraduate curricula but then suddenly explode all over the place in graduate chemistry or physics courses.
		Quantum Mechanics and Path Integrals by Richard Phillips Feynman and Alfred R. Hibbs.
		Feynman discovered and developed the application of the technique in his graduate dissertation, until one day legend has it (see the preface of Kleinert’s book) that Feynman realized that he couldn’t solve the quantum mechanical problem of the hydrogen atom using path integrals.
	diodati.omniscientx.com /a-theory-students-bookshelf (1838 words)

	Richard Feynman - Wikipedia, the free encyclopedia
		Feynman (in common with other famous physicists, Edward Teller and Albert Einstein) was a late talker; by his third birthday he had yet to utter a single word.
		Feynman gained great pleasure from coming up with such a "freshman level" explanation of the connection between spin and statistics (that groups of particles with spin 1/2 "repel", whereas groups with integer spin "clump"), a question he pondered in his own lectures and to which he demonstrated the solution in the 1986 Dirac memorial lecture.
		Feynman did not dispute the quark model; for example, when the fifth quark was discovered, Feynman immediately pointed out to his students that the discovery implied the existence of a sixth quark, which was duly discovered in the decade after his death.
	en.wikipedia.org /wiki/Feynman (5075 words)

	Richard Feynman \| Biography \| atomicarchive.com
		Feynman received a bachelor's degree from the Massachusetts Institute of Technology in 1939, and was named Putnam Fellow that same year.
		Feynman's collaboration on the latter with Murray Gell-Mann was seen as seminal, as the weak interaction was neatly described.
		Feynman is also known for his work on the Space Shuttle Challenger accident investigation, shocking the world by demonstrating the failure of the O-Rings.
	www.atomicarchive.com /Bios/Feynman.shtml (515 words)

	ICMP 2003: Path integrals and stochastic analysis [Sessions]
		In a first part, we define a Feynman path integral on a manifold as an Hida distribution, Wiener chaos being replaced by Chen iterated integrals.
		A survey of recent developements concerning rigorously defined infinite dimensional oscillatory integrals, "Feynman path integrals", is given.
		Functional integrals arising from 2-dimensional Yang-Mills and 3-dimensional Chern-Simons theory have deep connections with aspects of the structure of the moduli space of flat connections on a surface as well as some classical formulas in algebra due to Frobenius and Schur.
	icmp2003.net /sessions/pisa (749 words)

	Feynman's QED
		Physics had to wait for three young men, Feynman, Schwinger, and Tomonoga, filled with optimism and pessimism as the case may be from their experiences of the World War, to produce the correct formulation of quantum electrodynamics aka QED.
		One of Feynman's colleagues told me that the invitation showed that he took me seriously as a physicist, but while I was eager to tell Feynman my thoughts about Yang-Mills theory he only wanted my opinion on the legs of the dancing girls on stage.
		The path integral formalism was derived by the rather Zen procedure of introducing an infinite number of screens, drilling an infinite number of holes in each screen, thus ending up with no screen.
	www.kitp.ucsb.edu /~zee/feynman.html (3835 words)

	physical interpretation of Feynman path integral (Site not responding. Last check: 2007-10-18)
		So at every point on the path it is pointing somewhere or other, and all the paths are like that they all have little arrow pointing at some angle in the plane.
		The path integral does not result in a classical path; for then there would be no need for path integral in the first place.
		Which path integral ?For each physical system u have a path integral that gives u the amplitude of probability of transition from one quantum state to another...
	www.physicsforums.com /showthread.php?p=362282 (836 words)

	Path Integral on Spherical Surfaces in D Dimensions and on Group Spaces
		I solve the path integral for a point particle moving on the surface of a sphere in D dimensions and, exploiting the equivalence between a D=4 surface and the group space
		The purpose of the present note is to show that the new measure of path integration proposed in [4] finally solves the long-standing problems of the path integral on spheres and group spaces with results which are in agreement with the corresponding Lie algebras, as they should.
		Either (27) or (28) may be used as the correct path integral formulas in spaces with curvature and torsion.
	www.physik.fu-berlin.de /~kleinert/kleiner_re202/pisphere.html (1499 words)

	Shumway: Path Integral Methods
		Path integrals are sums over a continuum of variables.
		In physics, path integrals are used to sum over all possible trajectories of a particle, or over all possible fluctuations of a field.
		Path integrals also occur in other disciplines, such the Black-Scholes formula in economics, which prices an option by a sum over all possible financial variables.
	phy.asu.edu /shumway/pathintegrals.html (392 words)

	The 8th International Conference Path Integrals from Quantum Information to Cosmology, Prague, June 6-10 (Site not responding. Last check: 2007-10-18)
		In order to investigate its validity and usefulness, the path integral method was applied to hydrogen atom,the energy levels were calculated out with the same fine structure as the calculation of the Dirac wave equation, the electronic spin effect was also calculated out correctly when the hydrogen atom is put in a magnetic field.
		The path integral method would be useful for some physical systems when for which the Dirac equation can not be solved exactly, it was pointed out that the path integral method is a rapid quantum computation method.
		A path integral representation is given to the Green's function for the radial Dirac equation, by constructing a countably additive path space measure on the space of continuous paths living on the real half-line.
	www.jinr.ru /publish/Proceedings/Burdik-2005/index.html (3799 words)

	PATH INTEGRAL MONTE CARLO METHOD (Site not responding. Last check: 2007-10-18)
		A rigorous expression for the partition function of N identical fermions with spin 1/2 is obtained in a form suitable for Path Integral Monte Carlo (PIMC) simulation of a many electron system at finite temperature.
		Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented.
		Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations.
	www.fos.su.se /physical/sasha/pimc.html (521 words)

	Feynman Project 1
		Feynman’s answer: one needs to choose a unique oscillator solution x3 which gives exactly ½ of sum of advanced (i.e., from the future) and retarded (i.e., from the past) delayed classical actions at a distance between the toy electrons 1 and 2.
		Integral from past to present of oscillator pump force from 1 and 2 multiplied by influence functional.
		Feynman's Space-Time Picture of Non-Relativistic Quantum Mechanics in which the Born probability density is from the combined influence of advanced paths from the future meeting retarded paths from the past at a single event (x,t).
	www.qedcorp.com /pcr/pcr/feynman/feynpro1.html (7820 words)

	Richard P. Feynman
		I'd like to think of Feynman as someone who was delighted by the universe he lived in and the enigmas it presented to him.
		For, really, Feynman himself isn't the object of our (my) obsession and goal --- he is merely the purest image of the ambitious physicist who has much knowledge and still retains a child-like innocence in his view of the beauty and happiness of living.
		Feynman diagrams describe the interactions between particles predicted by a theory called QED (quantumelectrodynamics).
	members.tripod.com /abbynuss1/id32.htm (964 words)

	Sample Chapter for Feynman, R.P.: QED: The Strange Theory of Light and Matter.
		I enjoyed having Feynman explain to me why light moves in a straight line or how a focusing lens really works (on page 58: "A 'trick' can be played on Nature" by slowing light down along certain paths so the little arrows all turn by the same amount!).
		In fact, for most "practical" problems the path integral formalism is almost hopelessly involved, and in some cases downright impossible to use.
		What makes Feynman such an extraordinary physicist is that this "battle for the hearts and minds" I just described was between the crowd using Feynman diagrams versus a younger crowd using Feynman path integrals.
	www.pupress.princeton.edu /chapters/i8169.html (3880 words)

	Path integral molecular dynamics
		The extension of the path integral scheme to N particles in three dimensions is straightforward if it is assumed that the particles obey Boltzmann statistics, i.e., all spin statistics are neglected.
		It is worth mentioning that the path integral MD scheme outlined here has been combined with ab initio MD to yield an ab initio path integral Car-Parrinello method [101, 99].
		Finally, the path integral MD scheme has been modified to allow path integral simulations under conditions of constant temperature and pressure to be carried out [100].
	homepages.nyu.edu /~mt33/jpc_feat/node11.html (817 words)

	Path integral formulation - Wikipedia, the free encyclopedia
		If we realize that the Schrödinger equation is esentially a diffussion equation (but with imaginary time), then path integral is a method for the enumeration of random walks.
		For this reason path integrals had also been used in the study of Brownian motion and diffusion before they were introduced in quantum mechanics.
		Indeed, in the case of the Feynman path integral, the integration is over imaginary time, so the paths relevance to the particles real physical path, is open to debate.
	en.wikipedia.org /wiki/Feynman_path_integral (3248 words)

	Re: WKB approximation and Feynman Path Integral (Site not responding. Last check: 2007-10-18)
		According to quantum mechanics, particles are described by a complex wavefunction whose phase can be arbitrary, but as long as classical physics is a good starting point, the phase of the wavefunction can be determined in the semiclassical (=WKB) approximation.
		On the other hand, the path integral formulation of quantum mechanics sums over all possible histories of your system, and the weight is given by exp(iS/hbar) where S is the classical action of the configuration.
		Prev by thread: Re: WKB approximation and Feynman Path Integral
	www.lns.cornell.edu /spr/2004-02/msg0058609.html (247 words)

	Eduardo Mendel
		My research interests have dealt mainly with nonperturbative phenomena in Quantum Field Theory, as in lattice Quantum Chromo Dynamics at finite baryon densities and temperatures, where attempts are made to obtain nuclear matter from first principles in QCD.
		I have also worked on the Feynman path integral method in first quantization, where the Grand-canonical system of nucleons (many fermions) was simulated in order to study the nuclear condensation at high densities.
		For this we have also developed a method that can solve numerically the needed real-time Green's function based on a discretized version of the Path integral formalism.
	www.physik.uni-oldenburg.de /Docs/ftheorie/mendel.html (338 words)

	QT
		In this course we will review the fundamental ideas of quantum mechanics, introduce the path integral for a nonrelativistic point particle, and use it to derive time dependent perturbation theory and the Born series for nonrelativistic scattering.
		Time evolution: the amplitude for a path, the Feynman path integral, relation to the classical equations of motion and the Hamilton-Jacobi equations.
		Evaluating the path integral for the free particle and the harmonic oscillator.
	www.ph.ed.ac.uk /~rdb/QT.html (503 words)

	PREFACE
		Since that time, it has been united with statistical mechanics through Feynman's path integral, and its domain has been expanded to cover particle physics, condensed matter physics, astrophysics, and wherever path integrals are spoken.
		The last part, Chapters 15-19, introduces the Feynman path integral, and discusses "modern" subjects, including the physical approach to renormalization, spontaneous symmetry breaking, and topological excitations.
		have chosen to introduce path integrals only after the canonical approach is fully developed and applied.
	www.mit.edu /people/kerson/preface1.htm (735 words)

	Statistical Laboratory Seminars - Michaelmas Term 2000 (Site not responding. Last check: 2007-10-18)
		Since 1948, when Feynman introduced his famous path integral giving an explicit (but not rigorous) representation for the solutions of the Schroedinger equation, many mathematicians have contributed to the fascinating problem of how to give a rigorous meaning to this (infinite-dimensional) path integral.
		Secondly, a new construction will be given which allows to define a rigorous Feynman integral for very general Schroedinger equations including the cases of singular potentials and magnetic fields.
		The paths between any two data points are treated as missing data, utilizing the well known data augmentation algorithm.
	www.statslab.cam.ac.uk /Seminars/statsemmich2000.html (923 words)

	No Title
		We introduced the ideas of the propagator, the Feynman path integral and Feynman diagrams, in the context of quantum mechanics.
		We broke the propagation into more and more intermediate steps, ending with a limit in which the number of steps is infinite, and the paths are continuous curves.
		goes to zero, this results in the classical trajectory, for which the action is extremal -- thus making many contributions to the path integral which are all in phase, and which reinforce each other instead of cancelling due to a rapidly changing phase.
	www.emory.edu /PHYSICS/Faculty/Benson/380-96/notes/35/35.html (532 words)

	CiteULike: Tag feynman (Site not responding. Last check: 2007-10-18)
		Feynman Checkerboard as a Model of Discrete Space-Time
		posted to feynman history majorana path-integral physics quantum by ansobol as
		The Feynman graph representation of convolution semigroups and its applications to Levy statistics
	www.citeulike.org /tag/feynman (139 words)

	Re: WKB approximation and Feynman Path Integral (Site not responding. Last check: 2007-10-18)
		In article , Yi-Zen Chu; Yiren Qu wrote: > Hi everyone > > I notice that the wave function in the WKB approximation contain a > factor of exp[(-i/h) x Integral[2m(E - V)]], where the integral in the > exponent is really the action, since it satisfies the Hamilton-Jacobi > equation.
		Yes, actually you can get WKB from the Feynman path integral by a sort of steepest descent method when \hbar goes to zero (which is just the semi-classical situation).
		I think that whatever is your initial wave-function, in the limit of big times (such that the action becomes very big compared to \hbar) you get the WKB vawe-function.
	www.lns.cornell.edu /spr/2004-02/msg0058569.html (245 words)

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