Mathematical methods of non-Archimedean physics

Abstract

CONTENTS Introduction § 1. Generalized functions and Gaussian integrals on finite-dimensional non-Archimedean spaces § 2. Non-Archimedean Hilbert spaces § 3. Spaces of functions square-integrable with respect to Gauss and Lebesgue distributions on non-Archimedean spaces § 4. The Schrödinger and Bargmann-Fock representations in non-Archimedean quantum mechanics § 5. Non-Archimedean statistical quantum mechanics § 6. Existence and uniqueness theorems for the solution of linear partial differential equations on non-Archimedean spaces § 7. The solubility of Schrödinger's, Heisenberg's and Liouville's equations in non-Archimedean mechanics § 8. Trotter's formula in non-Archimedean commutative Banach algebras, and the chronological representation of the solution of Schrödinger's equation with a potential § 9. Generalized functions and Gaussian integrals on infinite-dimensional non-Archimedean spaces § 10. Existence and uniqueness theorems for the solution of linear partial differential equations on infinite-dimensional non-Archimedean spaces § 11. The path integral for a non-Archimedean scalar bosonic field § 12. Non-Archimedean bosonic strings in a photonic-like gauge § 13. Non-Archimedean bosonic string fields in a photonic-like gauge § 14. Singular functions of a non-Archimedean scalar bosonic field References