Toward the mathematical foundation of path integrals

Introduction

• What is path integral?
  
• Why is Euclidean path integral convenient? (under construction)
  
• Beginning nonstandard lattice path integral
• Beginning nonstandard smooth path integral

The simplest examples of nonstandard path integrals

• Bosonic harmonic oscilator 1 (piecewise linear path)
• Free scalar field in Minkowski space (smooth path)
  
• Free scalar field in Euclidean space (smooth path)
  
• Free electromagnetic field in Euclidean space (smooth path, Lorenz gauge)
  

Fermionic cases

• Elementary Grassmannian path integrals
  
• 2D Dirac equation in Minkowski space: T. Nakamura's approach (under construction)

Developing nonstandard methods of path integral

• Path integral in geometry (under construction)
• My Immature Ideas (under construction)