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Topic: Path integral

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	Path integral - Wikipedia, the free encyclopedia
		In mathematics, a path integral (also known as a line integral) is an integral where the function to be integrated is evaluated along a path or curve.
		The integral is then the limit of this sum, as the lengths of the subdivision intervals approach zero.
		However, path integrals in the sense of this article are important in quantum mechanics; for example, complex contour integration is often used in evaluating probability amplitudes in quantum scattering theory.
	en.wikipedia.org /wiki/Path_integral (708 words)

	PlanetMath: path integral (Site not responding. Last check: 2007-10-07)
		The path integral is a generalization of the integral that is very useful in theoretical and applied physics.
		A directed path integral on a closed path is denoted by summa and a circle with an arrow denoting direction.
		This is version 12 of path integral, born on 2002-02-03, modified 2004-09-10.
	planetmath.org /encyclopedia/PathIntegral.html (379 words)

	Path integral formulation - Wikipedia, the free encyclopedia
		The path integral formulation of quantum mechanics was developed in 1948 by Richard Feynman.
		The equal magnitude of all amplitudes in the path integral tends to make it difficult to define it such that it converges and is mathematically tractable.
		In one philosophical interpretation of quantum mechanics, the "sum over histories" interpretation, the path integral is taken to be fundamental and reality is viewed as a single indistinguishable "class" of paths which all share the same events.
	en.wikipedia.org /wiki/Path_integral_formulation (3038 words)

	PlanetMath: Feynman path integral (Site not responding. Last check: 2007-10-07)
		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, 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 11 of Feynman path integral, born on 2002-05-31, modified 2004-04-18.
	planetmath.org /encyclopedia/FeynmannPathIntegral.html (240 words)

	Relativistic Path Integrals & Random Flight
		The correct definition of the contributing amplitude for a path for the present relativistic case is phi = (i epsilon)^R where R is the number of reversals or corners along the path.
		Paths with the most reversals are few in number; similarly, paths with the fewest reversals.
		It is the invariant path length integral that is varied in the derivation of the Einstein equations by variational methods.
	graham.main.nc.us /~bhammel/FCCR/feynpath.html (2525 words)

	Chapters II-V of Quantum Mechanics
		And a point on the path at a particular time shall be the position of the particle.
		And because all paths are included, it shall be impossible to predict with certainty where an object be at a given moment.
		nd quantum tunnelling and barrier penetration shall be a consequence of the uncertainty of paths.
	www.jupiterscientific.org /science/baeparts/qm2345.html (1276 words)

	PATH INTEGRALS IN QUANTUM MECHANICS, STATISTICS, POLYMER PHYSICS, AND FINANCIAL MARKETS
		This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals.
		The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.
		The relevance of path integrals to financial markets is discussed, and improvements of the famous Black—Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.
	www.worldscibooks.com /physics/5057.html (607 words)

	Shumway: Path Integral Methods (Site not responding. Last check: 2007-10-07)
		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 (394 words)

	Dependent coordinates in path integral measure factorization
		The transformation of the path integral measure under the reduction procedure in dynamical systems with a symmetry is considered.
		Investigation is carried out in the case of the Wiener-type path integrals that are used for description of the diffusion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple unimodular Lie group.
		The transformation of the path integral, which factorizes the path integral measure, is based on the application of the optimal nonlinear filtering equation from the stochastic theory.
	stacks.iop.org /0305-4470/37/7019 (251 words)

	Path Integral (Site not responding. Last check: 2007-10-07)
		The path integral and the line integral are similar.
		If f is the field and p(t) is the path, the path integrand is f(p(t))×p′(t), as t runs from start to finish.
		The integral is ½(t-sin(2t)), from 0 to 2π, hence π.
	www.mathreference.com /ca-vec,pi.html (255 words)

	Path integral of a scalar-valued function*
		procedure for determining the length of a path, where we calculated the length of a slinky.
		For this reason, we often denote the integral representing the mass of the slinky as
		The two effects cancel and the integrals are equal.
	www.math.umn.edu /~nykamp/m2374/readings/pathint (832 words)

	Line integral of a vector field
		The line integral of a vector field will play a crucial role in the rest of the class.
		Out of the four fundamental theorems that form the cornerstones of the second half the course, three of the them involve line integrals of vector fields.
		(And the fourth involves surface integrals of vector fields, which are closely related to line integrals of vector fields.) I cannot emphasize too strongly the importance of these integrals.
	www.math.umn.edu /~nykamp/m2374/readings/lineint (564 words)

	The Path Integral For Dendritic Trees - LF, Gutmann (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		Abstract: We construct the path integral for determining the potential at any point on a dendritic tree of arbitrary geometry described by a linear cable equation.
		The path integral allows novel computational techniques to be applied to cable problems.
		Using the path integral, we have discovered simple diagrammatic rules for obtaining Green's functions on dendritic trees of arbitrary geometry.
	citeseer.ist.psu.edu /470619.html (400 words)

	Quantum Mechanics and Path Integrals
		The path integral formulation of quantum mechanics developed by Richard Feynman uses the so-called time-slicing technique.
		K(b,a) is the sum of all amplitude φ[x(t)] for each path x(t).
		Calculate the action of the path of a free particle in one dimension.
	quantummechanics.blogspot.com (438 words)

	Path integral molecular dynamics (optional reading)
		Recall that, according to the classical isomorphism, the path integral expression for the canonical partition function is isomorphic to the classical configuration integral for a certain P-particle system.
		It involves the use of a variable transformation of the formed used in previous lectures to do the path integral for the free-particle density matrix.
		Later on, when we discuss applications of path integrals, we will see why a formulation such as this for evaluating path integrals is advantageous.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_17/node5.html (672 words)

	eBay - path integral items on eBay.com (Site not responding. Last check: 2007-10-07)
		The Integral Being: A New Path to Personal Growth and M
		Path Integral Methods in Quantum Field Theory by R. a1_books
		Path Integral Methods in Quantum Field Theory - R *NEW
	search-desc.ebay.com /search/search.dll?query=path+integral&newu=1&... (185 words)

	Path integral for quantum operations
		In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary.
		We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation).
		We consider the path integral for quantum operation with a simple infinitesimal generator.
	stacks.iop.org /0305-4470/37/3241 (192 words)

	Path integral formalism (Site not responding. Last check: 2007-10-07)
		For a single particle this means, that it will travel along the classical path with a very high probability while all other paths are used with a very low probability.
		This means that the path integral extends over all paths: differentiable, non differentiable, smooth and even non smooth.
		The path integral method is formally easily extended to quantum field theory.
	www.unet.univie.ac.at /~a9405544/pages/qg_qft/node3.html (681 words)

	SSRN-Path Dependent Option Pricing: The Path Integral Partial Averaging Method by Andrew Matacz (Site not responding. Last check: 2007-10-07)
		Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process.
		For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one dimensional integral.
		Matacz, Andrew, "Path Dependent Option Pricing: The Path Integral Partial Averaging Method" (November 1999).
	papers.ssrn.com /sol3/papers.cfm?abstract_id=249570 (221 words)

	Sakurai's treatment of Feynman's Path Integral
		So the integral gives the propagator, which represents a transition amplitude.
		A great source for path integrals in general is "Techniques and Applications of Path Integration" by Schulman.
		Path integral methods is a powerful tool in Quantum field theory,
	www.physicsforums.com /showthread.php?p=802160 (384 words)

	Derivation of the discretized path integral
		We begin our discussion of the Feynman path integral with the canonical ensemble.
		When expressed in this way, the partition function, for a finite value of P, is isomorphic to a classical configuration integral for a P-particle system, that is a cyclic chain of particles, with harmonic nearest neighbor interactions and interacting with an external potential U(x)/P.
		Thus, for finite (if large) P the partition function in the discretized path integral representation can be treated as any ordinary classical configuration integral.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_14/node1.html (474 words)

	Path integral formulation of wave-optics
		,from path integral formulation),so should it be possible to argue from a path integral approach, that ray optics is the
		,all conceivable ray paths between any two fixed points are possible,so that there is an uncertainty in the ray path taken by light/sound in going from one point to the other.
		where n is the refraction index as a function of x,y,z,t...then the path integral for optics would be:
	www.physicsforums.com /showthread.php?p=961891#post961891 (508 words)

	More about Path Integral for Spin (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		Abstract: Path integral for the SU(2) spin system is reconsidered.
		We show that the Nielsen-Rohrlich(NR) formula is equivalent to the spin coherent state expression so that the phase space in the NR formalism is not topologically nontrivial.
		@misc{ funahashi-more, author = "Kunio Funahashi", title = "More about Path Integral for Spin", url = "citeseer.ist.psu.edu/131475.html" }
	citeseer.ist.psu.edu /131475.html (228 words)

	Citebase - Q-Deformed Path Integral
		Authors: Chaichian, M. Demichev, A. Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q, we construct path integral representation for the quantum mechanical evolution operator kernel of q-oscillator.
		Comment: 12 pages, latex, minor changes and refs.
		Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral [ Abstract, 2 Cites, Cached PDF ]
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/9310001 (940 words)

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