Multiparticle states in braided lightlike κ -Minkowski noncommutative QFT

In this study, we construct a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>-dimensional, relativistic, free, complex scalar quantum field theory on the noncommutative spacetime known as lightlike <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>κ</c:mi></c:math>-Minkowski. The associated <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>κ</e:mi></e:mrow></e:math>-Poincaré quantum group of isometries is triangular, and its quantum R matrix enables the definition of a braided algebra of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>N</g:mi></g:mrow></g:math> points that retains <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>κ</i:mi></i:mrow></i:math>-Poincaré invariance. Leveraging our recent findings, we can now represent the generators of the deformed oscillator algebra as nonlinear redefinitions of undeformed oscillators, which are nonlocal in momentum space. The deformations manifest at the multiparticle level, as the one-particle states are identical to the undeformed ones. We successfully introduce a covariant and involutive deformed flip operator using the R matrix. The corresponding deformed (anti)symmetrization operators are covariant and idempotent, allowing for a well-posed definition of multiparticle states, a result long sought in quantum field theory on <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>κ</k:mi></k:mrow></k:math>-Minkowski. We find that <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>P</m:mi></m:mrow></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mi>T</o:mi></o:mrow></o:math> are not symmetries of the theory, although <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mi>P</q:mi><q:mi>T</q:mi></q:mrow></q:math> (and hence <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi>C</s:mi><s:mi>P</s:mi><s:mi>T</s:mi></s:mrow></s:math>) is. We conclude by noticing that identical particles appear distinguishable in the new theory, and discuss the fate of the Pauli exclusion principle in this setting. Published by the American Physical Society 2024