Approximation schemes for path integration on Riemannian manifolds
| dc.contributor.author | Sampedro Pascual, Juan Carlos | |
| dc.date.accessioned | 2023-06-22T10:44:06Z | |
| dc.date.available | 2023-06-22T10:44:06Z | |
| dc.date.issued | 2022-03-21 | |
| dc.description | CRUE-CSIC (Acuerdos Transformativos 2022) | |
| dc.description.abstract | In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for L1-functionals, of the approach followed by Andersson and Driver on [1]. We follow a new approach motived by the categorical concept of colimit. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.sponsorship | Gobierno vasco | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/72540 | |
| dc.identifier.doi | 10.1016/j.jmaa.2022.126176 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.jmaa.2022.126176 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/71541 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of Mathematical Analysis and Applications | |
| dc.language.iso | eng | |
| dc.page.initial | 126176 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PGC2018-097104-B-I00 | |
| dc.relation.projectID | PRE2019_1_0220 | |
| dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
| dc.subject.cdu | 51 | |
| dc.subject.keyword | Colimit | |
| dc.subject.keyword | Finite dimensional approximations | |
| dc.subject.keyword | Riemannian manifolds | |
| dc.subject.keyword | Stratonovich stochastic integral | |
| dc.subject.keyword | Wiener measure | |
| dc.subject.ucm | Análisis numérico | |
| dc.subject.ucm | Procesos estocásticos | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1206 Análisis Numérico | |
| dc.subject.unesco | 1208.08 Procesos Estocásticos | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Approximation schemes for path integration on Riemannian manifolds | |
| dc.type | journal article | |
| dc.volume.number | 512 | |
| dcterms.references | 1] L. Andersson, B.K. Driver, Finite dimensional approximations to Wiener measure and path integral formulas on manifolds, J. Funct. Anal. 165 (2) (1999) 430–498. [2] C. Bär, Renormalized integrals and a path integral formula for the heat kernel on a manifold, in: Analysis, Geometry and Quantum Field Theory, in: Contemp. Math., vol. 584, Amer. Math. Soc., Providence, RI, 2012, pp. 179–197. [3] C. Bär, F. Pfäffle, Path integrals on manifolds by finite dimensional approximation, J. Reine Angew. Math. 625 (2008) 29–57. [4] C. Bär, F. Pfäffle, Wiener measures on Riemannian manifolds and the Feynman-Kac formula, Mat. Contemp. 40 (2011) 37–90. [5] J.M.F. Castillo, The Hitchhiker guide to categorical Banach space theory. Part I, Extr. Math. 25 (2) (2010) 103–149. [6] D.L. Cohn, Measure Theory, Springer, New York, 2013. [7] P.J. Daniell, A general form of integral, Ann. Math. (2) 19 (4) (June 1918) 279–294. [8] P.J. Daniell, Integrals in an infinite number of dimensions, Ann. Math. (2) 20 (4) (July 1919) 281–288. [9] P.J. Daniell, Functions of limited variation in an infinite number of dimension, Ann. Math. (2) 21 (1) (September 1919) 30–38. [10] R. Feynman, Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys. 20 (2) (April 1948) 367–387. [11] R. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, 1965. [12] G.B. Folland, Real Analysis, Modern Techniques and Their Applications, second edition, John Wiley & Sons, Inc., 1999. [13] A. Grigor’yan, Heat Kernel and Analysis on Manifolds, Studies in Advanced Mathematics, vol. 47, American Mathematical Society, 2009. [14] E.P. Hsu, Stochastic Analysis on Manifolds, Graduate Studies in Mathematics, vol. 38, 2002. [15] B. Jessen, The theory of integration in a space of infinite number of dimensions, Acta Math. 63 (December 1934) 249–323. [16] A.P.C. Lim, Path integrals on a compact manifold with non-negative curvature, Rev. Math. Phys. 19 (09) (2007) 967–1044. [17] M. Ludewig, Path integrals on manifolds with boundary, Commun. Math. Phys. 354 (2) (2016) 621–640. [18] M. Ludewig, Heat kernel asymptotics, path integrals and infinite-dimensional determinants, J. Geom. Phys. 131 (2018) 66–88. [19] M. Ludewig, Strong short-time asymptotics and convolution approximation of the heat kernel, Ann. Glob. Anal. Geom. 55 (2) (2019) 371–394. [20] R. Peled, Notes on sigma algebras for Brownian motion course, Lecture Notes, http://www.math.tau.ac.il/~peledron/ Teaching/Brownian_motion/Sigma_algebra_notes.pdf. [21] P.E. Protter, Stochastic Integration and Differential Equations, 2nd edition, Springer-Verlag, 2004. [22] E. Riehl, Category Theory in Context, Dover Publications, 2016. [23] J.C. Sampedro, On the space of infinite dimensional integrable functions, J. Math. Anal. Appl. 488 (1) (2020). [24] N.E. Wegge-Olsen, K-Theory and C*-Algebras, A Friendly Approach, Oxford University Press, 1993. [25] N. Wiener, The mean of a functional of arbitrary elements, in: Annals of Mathematics, in: Second Series, vol. 22, 1920, pp. 66–72. [26] N. Wiener, The average value of an analytic functional, Proc. Natl. Acad. Sci. USA 7 (1921) 253–260. [27] N. Wiener, The average of an analytic functional and the Brownian movement, Proc. Natl. Acad. Sci. USA 7 (1921) 294–298. [28] N. Wiener, Differential space, J. Math. Phys. 2 (1923) 131–174. [29] N. Wiener, The average value of a functional, Proc. Lond. Math. Soc. (2) 22 (1924) 454–467. [30] N. Wiener, Generalized harmonic analysis, Acta Math. 55 (1930) 117–258. [31] Y. Yamasaki, Measures on Infinite-Dimensional Spaces, World Scientific Publishing Co., Singapore, 1985. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5110d385-d47f-4760-a4df-4efc25bdf631 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5110d385-d47f-4760-a4df-4efc25bdf631 |
Download
Original bundle
1 - 1 of 1
Loading...
- Name:
- 1-s2.0-S0022247X22001901-main.pdf
- Size:
- 449.03 KB
- Format:
- Adobe Portable Document Format
