### Author

Vaclav Kosar

### Introduction

This paper is summary and enhancement of existing rather scattered literature regarding finite-dimensional quantum mechanics. In the later parts Feynman’s path summation is discussed.

Purpose of chapter 1 is to get familiar with finite-dimensional appoximation operator using discrete Fourier transformation as an example. In chapter 2 idea of inducing discrete kinematics using pair of mappings is discussed for special case of Schwinger approximation on flat configuration manifold R. In chapter 3 convergence question for defined Hilbert space imbedding of Swinger approximation on R is discussed. In chapter 4 most intuitive discrete-time evolution definitions are discussed. Special attention is paid to Feynman’s path integral. Feynman’s checkerboard problem closely connected to Feynman’s path integral is also included in this chapter.