Hyperbolic Vacua in Minkowski Space

TL;DR

This paper constructs new Lorentz-invariant vacua for a massless scalar field in Minkowski space, generalizing the Rindler vacuum and revealing connections to de Sitter $ extalpha$-vacua with unique symmetry properties.

Contribution

It introduces a family of Lorentz-invariant vacua extending the Rindler vacuum, with explicit formulations and links to de Sitter $ extalpha$-vacua, enhancing understanding of vacuum structures in Minkowski space.

Findings

Constructed Lorentz, not Poincare, invariant vacua.

Expressed vacua as squeezed states of the Poincare vacuum.

Connected Minkowski vacua to de Sitter $ extalpha$-vacua with antipodal singularities.

Abstract

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter $\alpha$-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.