<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mtext>−</mml:mtext><mml:mi>P</mml:mi><mml:mtext /><mml:mtext /><mml:mtext>−</mml:mtext><mml:mi>T</mml:mi></mml:mrow></mml:math> fractionalization

نویسندگان

چکیده

Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as $\mathbb{Z}_2$-involutions in the passive transformation on coordinates; but together with a charge conjugation C, total C-P-R-T have enriched active transformations fields representations spacetime-internal symmetry groups quantum field theories (QFTs). In this work, we derive that these can be further fractionalized, especially presence fermion $(-1)^{\rm F}$. We elaborate examples including relativistic Lorentz invariant QFTs (e.g., spin-1/2 Dirac Majorana spinor theories) nonrelativistic many-body systems (involving zero modes), comment applications to spin-1 Maxwell electromagnetism (QED) interacting Yang-Mills (QCD) gauge theories. discover various C-P-R-T-$(-1)^{\rm F}$ group structures, e.g., is projective representation $\mathbb{Z}_2^{\rm C}\times \mathbb{Z}_2^{\rm P} \times T}$ an (anti)linear order-16 nonabelian finite group, central product between order-8 dihedral (generated by C P) quaternion order-4 generated T T$^2=(-1)^{\rm The general theme may coined C-P-T C-R-T fractionalization.

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ژورنال

عنوان ژورنال: Physical review

سال: 2022

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physrevd.106.105009