<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:mrow></mml:math> symmetric fermionic particle oscillations in even dimensional rep

We describe a novel class of quantum mechanical particle oscillations in both relativistic and nonrelativistic systems based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="script">P</a:mi><a:mi mathvariant="script">T</a:mi></a:mrow></a:math> symmetry and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi mathvariant="script">T</e:mi><e:mn>2</e:mn></e:msup><e:mo>=</e:mo><e:mo>−</e:mo><e:mn>1</e:mn></e:math> (relevant for fermions), where <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="script">P</h:mi></h:math> is parity and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">T</k:mi></k:math> is time reversal. The Hamiltonians are chosen at the outset to be self-adjoint with respect to a <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:mi mathvariant="script">P</n:mi><n:mi mathvariant="script">T</n:mi></n:mrow></n:math> inner product. The quantum mechanical time evolution is based on a modified <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mi mathvariant="script">C</r:mi><r:mi mathvariant="script">P</r:mi><r:mi mathvariant="script">T</r:mi></r:mrow></r:math> inner product constructed in terms of a suitable <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi mathvariant="script">C</w:mi></w:math> operator. The resulting quantum mechanical evolution is shown to be unitary and probability is conserved by the oscillations. Published by the American Physical Society 2024