The Tachyon Propagator

TL;DR

This paper develops a canonical quantization framework for tachyon fields, revealing a unique unbounded energy spectrum and establishing a connection between vacuum expectation values and principal-value Green's functions.

Contribution

It introduces a quantization scheme for tachyon fields and constructs a Fock space with a zero-energy eigenfunction, highlighting differences from bradyon quantization.

Findings

Constructed a tachyon field Hamiltonian and operators.

Identified a unbounded energy spectrum for tachyons.

Connected vacuum expectation values to principal-value Green's functions.

Abstract

Following the canonical quantization procedure for a tachyon field, the usual Hamiltonian and the creation and annihilation operators are obtained. The observation that the mass hyperboloid $p^2-m^2=0$ is one-sheeted, as opposed to the case of bradyons where $p^2+m^2=0$ is two-sheeted, leads to the construction of a base which is unbounded for negative as well as for positive energies. There is a zero-energy eigenfunction from which all other states can be constructed by repeated application of decreasing or increasing operators, within this Fock space the vacuum expectation value of the chronological product of field operators is shown to coincide with Cauchy's principal-value Green's function.