Related papers: C, P, T, and Triality
In usual extended technicolor (ETC) theories based on the group ${\rm{SU}(N_{ETC}})_{ETC}$, the quarks of charge 2/3 and -1/3 and the charged leptons of all generations arise from ETC fermion multiplets transforming according to the…
We develop a charge-parity-time (CPT) frameness resource theory to circumvent CPT- superselection. We construct and quantify such resources for spins 0, 1/2, and 1 and for Majorana particles, and we show that spin 0 particles only admit…
A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic…
We develop a complete resource theory of charge-parity-time (CPT) inversion symmetry for both massive and massless relativistic particles of arbitrary spin. We show that a unitary representation of CPT can be consistently constructed for…
Symmetry protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For non-interacting fermion systems with time…
Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define seven binary eigenvalues that distinguish the $2^7=128$ states of 32 fermions, and determine their parity, electric charge and interactions. Three commuting elements of the…
We consider the triality fusion category discovered in the $c = 1$ KT theory \cite{Thorngren:2021yso}. We analyze this fusion category using the tools from the group theoretical fusion category and describe how to compute the simple lines,…
We investigate a parity-time (PT) symmetric system that consists of two symmetrically coupled asymmetric dimers. The enclosed magnetic flux controls the PT phase transition. The system can reenter the exact PT-symmetric phase from a broken…
Based on the original meanings of C, P, T transformations, a more perfect and rational scheme is advanced. According to new scheme, the propagation function of Femion would change a negative sign under C, T transformations, while that of…
It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic…
A group structure of the discrete transformations (parity, time reversal and charge conjugation) for spinor field in de Sitter space are studied in terms of extraspecial finite groups. Two $CPT$ groups are introduced, the first group from…
Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role in the quantization of the superstring,…
We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand,…
We consider the transformation properties of fermions under the discrete symmetries CPT, CP, and C in the presence of B-L violation. We thus generalize the analysis of the known properties of Majorana neutrinos, probed via neutrinoless…
In a space with some sufficiently small compact dimension (with non-trivial cycles) and with periodic boundary conditions for the fermions, the charge conjugation (C), spatial parity (P), time reversal (T) and CPT symmetries are…
In this work, we present new connections between three types of quantum states: positive under partial transpose states, symmetric with positive coefficients states and invariant under realignment states. First, we obtain a common upper…
Recently, it has been shown that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry $G$ can be completely classified by the group cohomology class $H^3(G, \mathrm{U}(1))$. Later, group…
We studied parity-time (PT) symmetric trimer systems that feature open and closed boundaries. The exceptional point is three-state coalescence at zero energy because of chiral symmetry in the open trimer; however, two-state coalescence…
It is shown that the Dirac theory implies complex space-time and complex space-time can lead to the Dirac equation. It is suggested that fermions are grouped into doublets, those doublets are then divided into color singlets (leptons) and…
Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency conditions and a natural embedding of the…