zbMATH — the first resource for mathematics

A review of finite approximations, Archimedean and non-Archimedean. (English) Zbl 1457.81046
Summary: We give a review of finite approximations of quantum systems, both in an Archimedean and a non-Archimedean setting. Proofs will generally be omitted. In the Appendix we present some numerical results.
81Q15 Perturbation theories for operators and differential equations in quantum theory
35A35 Theoretical approximation in context of PDEs
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47A58 Linear operator approximation theory
Full Text: DOI
[1] Albeverio, S.; Gordon, E. I.; Khrennikov, A. Yu., Finite-dimensional approximations of operators in the Hilbert spaces of functions on locally compact abelian groups, Acta Appl.Math., 64, 33-73, (2000) · Zbl 1019.47020
[2] E. M. Bakken, Finite Approximations of Quantum Systems in a non-Archimedian and Archimedian Setting, PhD dissertation, The Norwegian University of Science and Technology (NTNU) (Trondheim, Norway, August 2016).
[3] Bakken, E. M.; Digernes, T., Finite approximations of physical models over local fields, p-Adic Numbers Ultrametric Anal. Appl., 7, 245-258, (2015) · Zbl 1345.47067
[4] Bakken, E. M.; Digernes, T.; Weisbart, D., Brownian motion and finite approximations of quantum systems over local fields, Rev. Math. Phys., 29, 1750016, (2017) · Zbl 1370.81068
[5] Digernes, T.; Varadarajan, V. S.; Varadhan, S. R. S., Finite approximations to quantum systems, Rev. Math. Phys., 6, 621-648, (1994) · Zbl 0855.47046
[6] A. N. Kochubei, Pseudo-Differential Equations and Stochastics over non-Archimedean fields, Monographs and Textbooks in Pure and AppliedMathematics 244 (Marcel Dekker Inc., New York, 2001).
[7] Varadarajan, V. S., Path integrals for a class of p-adic Schrödinger equations, Lett. Math. Phys., 39, 97-106, (1997) · Zbl 0868.47047
[8] V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (World Scientific Publishing Co. Inc., River Edge, NJ, 1994). · Zbl 0812.46076
[9] A. Weil, Basic Number Theory, third ed., Die Grundlehren der Mathematischen Wissenschaften, Band 144 (Springer-Verlag, New York-Berlin, 1974). · Zbl 0326.12001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.