My Notes On Path Integrals To Quantum Mechanics
What makes Feynmann’s Path Integrals an alternative statement of Quantum Physics.
What I observed is,
1. Discretization is at the heart of path integral. So it is in Rieman integral, a sum of tiny rectangles for area under a curve of th function, definitely a discretization process. When the number of such small rectangles tends to infinity, it becomes pure mathematics, acceptable for all standards irrespective of experimenters. And ‘discretization’ explains Quantum Physics.

Path integral is sum of action over all possible paths between two points or two events; which tends to the Euler-Lagrange path of least action in the classical limit.
2. The Gaussian distribution brings out true the true face of infinite number of random events; the distribution is definite, not random. Even probability of heads and tails in simple tossing of a coin tends to 50%, a definite number, when the number of tosses tends to infinity and tosses are perfectly random. The maxwell-Boltzmann distribution of random velocities of particles in a box , is a definite pattern, born out of perfect randomness of particles’ velocities. The search for ‘what we can determine or measure’ in random ensemble of probabilities ends in statistical inferences , definiteness of laws. This is at the foundation of quantum physics. Therefore Feynmann’s path integral method is a fundamental, powerful, easily explained and convincing explanation of Quantum physics.

Thus Feynmann’s path integral concept explains quantum physics more convincingly than any other method of quantum physics.