Results 211 to 220 of about 3,163 (263)
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2008
AbstractThis chapter presents a short review of path integrals in quantum mechanics. This is followed by a detailed discussion of the evaluation of the semi-classical propagator, involving quadratic expansions of the action and the calculation of determinants. The concept of functionals is introduced for multi-dimensional cases, using a system linearly
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AbstractThis chapter presents a short review of path integrals in quantum mechanics. This is followed by a detailed discussion of the evaluation of the semi-classical propagator, involving quadratic expansions of the action and the calculation of determinants. The concept of functionals is introduced for multi-dimensional cases, using a system linearly
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Journal of Mathematical Physics, 2000
Three approaches to functional integration are compared: Feynman’s definition and the Feynman–Kac formula, Bryce DeWitt’s formalism, and the authors’ axiomatic scheme. They serve to highlight the evolution of functional integration in the second half of the twentieth century.
Cartier, Pierre, DeWitt-Morette, Cécile
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Three approaches to functional integration are compared: Feynman’s definition and the Feynman–Kac formula, Bryce DeWitt’s formalism, and the authors’ axiomatic scheme. They serve to highlight the evolution of functional integration in the second half of the twentieth century.
Cartier, Pierre, DeWitt-Morette, Cécile
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2006
Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed,
Pierre Cartier, Cecile DeWitt-Morette
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Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed,
Pierre Cartier, Cecile DeWitt-Morette
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Functional Integration; Path Integrals
2009If the variable of integration is a field, a functional integral is sometimes called “a sum over histories”. Functional integration is a rich and powerful mathematical technique because the domain of integration X is an infinite dimensional space. Short of having intuitive understanding of infinite dimensional spaces of functions, we have extensive ...
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Thermodynamic functions as correlation-function integrals
The Journal of Chemical Physics, 2013Expressions of some thermodynamic functions as correlation-function integrals, such as the Ornstein-Zernike integral, the Kirkwood-Buff integrals, and the integral formulas for virial coefficients, are recalled. It is noted, as has been remarked before, that the choice of molecular centers from which intermolecular distances are measured is arbitrary ...
K, Koga, B, Widom
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Notes on Functional Integration
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Integration of Interval Functions
SIAM Journal on Mathematical Analysis, 1981An interval function Y assigns an interval $Y(x) = (y(x),\bar y(x)]$ in the extended real number system to each x in its interval $X = [a,b]$ of definition. The integral of Y over $[a,b]$ is taken to be the interval $\int_a^b {Y(x)dx = [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\int } _a^b \underset{\raise0.3em\hbox{$\smash ...
Caprani, Ole, Madsen, Kaj, Rall, L. B.
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Integrating function and mechanism
Trends in Ecology & Evolution, 2009Behavioural ecology often makes the assumption that animals can respond flexibly by adopting the optimal behaviour for each circumstance. However, as ethologists have long known, behaviour is determined by mechanisms that are not optimal in every circumstance. As we discuss here, we believe that it is necessary to integrate these separate traditions by
McNamara, JM, Houston, AI
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Integrating Functional Genomics Data
2008The revolution in high throughput biology experiments producing genome-scale data has heightened the challenge of integrating functional genomics data. Data integration is essential for making reliable inferences from functional genomics data, as the datasets are neither error-free nor comprehensive.
Insuk, Lee, Edward M, Marcotte
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Integrating functional genomics data
Biochemical Society Transactions, 2003Functional annotation of fully sequenced genomes is still a major issue. High-throughput data sets could be used to provide more and better functional annotations. However differences in data quality need to be taken into account. For this purpose these high-throughput data sets need to be integrated so that the data quality can be assessed, hypotheses
P, Kemmeren, F C P, Holstege
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