Khrennikov, A. Yu. The Schrödinger and Bargmann-Fock representations in non-Archimedean quantum mechanics. (English. Russian original) Zbl 0749.46046 Sov. Phys., Dokl. 35, No. 7, 638-640 (1990); translation from Dokl. Akad. Nauk SSSR 313, No. 2, 325-329 (1990). Summary: We develop the mathematical apparatus of quantization with wave functions taking values in a non-Archimedean field \(K\). We construct a theory of generalized functions ( distributions) and integration in a non- Archimedean space \(K\). We introduce the function spaces \(L_ 2(K^ n,dx)\) and \(L_ 2(Z^ n,e^{-z\bar z} dz d\bar z)\), where \(Z\) is a quadratic extension of the field \(K\), and in those spaces we realize (with the aid of a calculus of pseudo-differential operators) the Schrödinger and Bargmann-Fock representations. Cited in 6 Documents MSC: 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 46N50 Applications of functional analysis in quantum physics 81S99 General quantum mechanics and problems of quantization 46F10 Operations with distributions and generalized functions Keywords:quantization; wave functions taking values in a non-Archimedean field; generalized functions; distributions; integration; pseudo-differential operators; Schrödinger and Bargmann-Fock representations PDFBibTeX XMLCite \textit{A. Yu. Khrennikov}, Sov. Phys., Dokl. 35, No. 7, 638--640 (1990; Zbl 0749.46046); translation from Dokl. Akad. Nauk SSSR 313, No. 2, 325--329 (1990)