Proper scalar product for tachyon representations in configuration space

DOI: 
10.1103/PhysRevD.102.125010
Publication date: 
03/12/2020
Main author: 
López-Ruiz, F. F.
IAA authors: 
Aldaya, V.
Authors: 
López-Ruiz, F. F.;Guerrero, J.;Aldaya, V.
Journal: 
Physical Review D
Refereed: 
Yes
Publication type: 
Article
Volume: 
102
Pages: 
125010
Abstract: 
We propose a new inner product for scalar fields that are solutions of the Klein-Gordon equation with m<SUP>2</SUP>&lt;0 . This inner product is nonlocal, bearing an integral kernel including Bessel functions of the second kind. The associated norm proves to be positive definite in the subspace of oscillatory solutions, as opposed to the conventional one, although some regularization procedure is required. Poincaré transformations are unitarily implemented on this subspace, which is the support of a unitary and irreducible representation of the proper orthochronous Poincaré group. We also provide a new Fourier transform between configuration and momentum spaces, which is unitary, and recover the projection onto the representation space. This new scenario suggests a revision of the corresponding quantum field theory.
Database: 
ADS
URL: 
https://ui.adsabs.harvard.edu/#abs/2020PhRvD.102l5010L/abstract
ADS Bibcode: 
2020PhRvD.102l5010L
Keywords: 
High Energy Physics - Theory;Mathematical Physics;Quantum Physics