A modification of the projective construction of quantum states for field theories

TL;DR

This paper proposes a slight modification to the projective construction of quantum states for field theories, addressing potential flaws where the original method might produce inadequate state spaces for quantization.

Contribution

It introduces a refined construction method that avoids the issue of producing too small quantum state spaces in field theory quantization.

Findings

Modified construction is free from the flaw of small state spaces

Ensures more complete quantum state spaces for field theories

Addresses limitations of previous projective construction methods

Abstract

The projective construction of quantum states for field theories may be flawed--in some cases the construction may possibly lead to spaces of quantum states which are "too small" to be used in quantization of field theories. Here we present a slight modification of the construction which is free from this flaw.