On the problem of time in two and four dimensions

TL;DR

This paper discusses the problem of time in general-covariant theories and proposes a mechanism in string theory that could resolve this issue in four dimensions, challenging common assumptions about gauge symmetries.

Contribution

It introduces a novel approach suggesting that the problem of time can be addressed through conformal anomalies in string theory, offering a new perspective on gauge symmetries.

Findings

In subcritical free string, the Hamiltonian is no longer a constraint after quantization.

The proposed mechanism may resolve the problem of time in four-dimensional theories.

Challenges the belief that all gauge symmetries are mere redundancies.

Abstract

In general-covariant theories the Hamiltonian is a constraint, and hence there is no time evolution; this is the problem of time. In the subcritical free string, the Hamiltonian ceases to be a constraint after quantization due to conformal anomalies, and time evolution becomes non-trivial and unitary. It is argued that the problem of time in four dimensions can be resolved by a similar mechanism. This forces us to challenge some widespread beliefs, such as the idea that every gauge symmetry is a redundancy of the description.