Quantum Physics has a New, and Remarkable, Expansion

TL;DR

This paper introduces affine quantization, an expansion of canonical quantization, capable of accurately solving problems like the half-harmonic oscillator and extending to field theory and gravity.

Contribution

It presents affine quantization as a novel method that overcomes limitations of canonical quantization, enabling solutions to previously unsolvable quantum problems.

Findings

Affine quantization correctly solves the half-harmonic oscillator.

It extends to field theory and gravity applications.

Provides foundational understanding of affine quantization.

Abstract

Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then it quickly bounces backwards. This second model cannot be correctly solved using canonical quantization. Now, there is an expansion of quantization, called affine quantization, that can correctly solve the half-harmonic oscillator, and offers correct solutions to a grand collection of other problems, which even reaches to field theory and gravity. This paper has been designed to introduce affine quantization; what it is, and what it can do.