Deformation quantization and the tomographic representation of quantum fields

TL;DR

This paper develops a tomographic representation of quantum fields using deformation quantization, introducing new tools like the symplectic tomogram and star product, with potential applications in quantum cosmology and gravity.

Contribution

It constructs a novel tomographic framework for quantum fields within deformation quantization, including the Wigner functional, symplectic tomogram, and star product, extending quantum field analysis methods.

Findings

Introduces the symplectic tomogram for quantum fields.

Derives the tomographic star product functional integral.

Discusses applications to loop quantum cosmology and gravity.

Abstract

The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic star product is determined. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are briefly discussed.