Quantum Fields with Noncommutative Target Spaces

TL;DR

This paper investigates quantum field theories with noncommutative target spaces, revealing a deformed black body spectrum at high frequencies that could impact astrophysical observations and the understanding of noncommutative geometries.

Contribution

It introduces and analyzes QFTs with noncommutative target spaces, deriving a deformed black body spectrum and exploring potential observational consequences.

Findings

Deformed black body spectrum at high frequencies

Potential impact on GZK cut-off calculations

Connection between noncommutative geometry and spectral deformation

Abstract

Quantum field theories (QFT's) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT's with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [1], and others [2,3,4,5,6,7,8]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al [9,10]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed black body spectrum, which is analysed in detail. The difference between the usual and the deformed black body spectrum appears in the region of high frequencies. Therefore we expect that the deformed black body radiation may potentially be used to compute a GZK cut-off which will depend on the noncommutative parameter $\theta$.