# Derivation of Quantum Theory from Feynman's Rules

**Authors:** Philip Goyal  
**arXiv:** [1403.3527](https://arxiv.org/abs/1403.3527)  
**Date:** 2014-03-14  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1403.3527v1/

## Key points

- Philip Goyal's paper explores Richard Feynman's formulation of quantum theory
- Feynman's formulation lacks the mathematical structure of the standard von Neumann-Dirac formalism, specifically in regards to unitary evolution
- Goyal presents a method to reconstruct the finite-dimensional quantum formalism using Feynman's rules and introduces the no-disturbance postulate
- The no-disturbance postulate states that certain measurements have no impact on subsequent measurement outcomes
- By incorporating this postulate, Goyal successfully derives both the amplitude rule for composite systems and Dirac's amplitude-action rule based on a single elementary assumption aligned with Feynman's rules
- Goyal's work expands upon Feynman's formulation by incorporating essential mathematical structures from the von Neumann-Dirac formalism through consistent assumptions.

## Summary

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Philip Goyal's paper "Derivation of Quantum Theory from Feynman's Rules" explores Richard Feynman's formulation of quantum theory. While known for its simplicity and computational power, this formulation lacks the fundamental mathematical structure of the standard von Neumann-Dirac formalism, specifically in regards to unitary evolution. To address this limitation, Goyal presents a method to reconstruct the finite-dimensional quantum formalism using Feynman's rules and introduces the no-disturbance postulate. This postulate states that certain measurements have no impact on subsequent measurement outcomes. By incorporating this postulate, Goyal successfully derives both the amplitude rule for composite systems and Dirac's amplitude-action rule based on a single elementary assumption aligned with Feynman's rules. Overall, Goyal's work expands upon Feynman's formulation by incorporating essential mathematical structures from the von Neumann-Dirac formalism through consistent assumptions.