Related papers: C, P, T, and Triality
$CPT$ groups for spinor fields in de Sitter and anti-de Sitter spaces are defined in the framework of automorphism groups of Clifford algebras. It is shown that de Sitter spaces with mutually opposite signatures correspond to Clifford…
Based on a study of {\it charge,} (C), {\it parity} (P) and {\it time reversal} (T) symmetries we show how a CP violating network of defects in the early Universe may bias baryon number production. A static network, even though it violates…
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass…
We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations.…
A noteworthy discovery is that the minimal evolution time is smaller for parity-time ($\mathcal{PT}$) symmetric systems compared to Hermitian setups. Moreover, there is a significant acceleration of two-qubit quantum entanglement…
Invariance under the combined transformations of CPT (in any order) is guaranteed in Quantum Field Theory in flat space times due to a basic theorem (CPT Theorem). The currently used formalism of particle physics phenomenology is based on…
Quantum anomalies, breakdown of classical symmetries by quantum effects, provide a sharp definition of symmetry protected topological phases. In particular, they can diagnose interaction effects on the non-interacting classification of…
Trialitarian triples are triples of central simple algebras of degree 8 with orthogonal involution that provide a convenient structure for the representation of trialitarian algebraic groups as automorphism groups. This paper explicitly…
The four dimensional Causal Dynamical Triangulations (CDT) approach to quantum gravity is already more than ten years old theory with numerous unprecedented predictions such as non-trivial phase structure of gravitational field and…
We have studied the different symmetric properties of the generalized Maxwell's - Dirac equation along with their quantum properties. Applying the parity (\mathcal{P}), time reversal (\mathcal{T}), charge conjugation (\mathcal{C}) and their…
Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some…
We discuss the importance of the CP (simultaneous particle-antiparticle and left-right permutation) and T (time reversal) symmetries in the context of fundamental interactions. We show that they may provide clues to go beyond the 4-D gauge…
A triality is a sort of super-symmetry that exchanges the types of the elements of an incidence geometry in cycles of length three. Although geometries with trialities exhibit fascinating behaviors, their construction is challenging, making…
A quantitative prediction of Conformal Field Theory (CFT), which relates the second moment of the energy-density correlator away from criticality to the value of the central charge, is verified in the sine-Gordon model. By exploiting the…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
Under the assumptions that $SU(3)_c\times U(1)_Y \times G^{\prime}$ with $G^{\prime}$ simple is a local symmetry group at high energies, that color is parity-conserving, and the Y-charges are irreducible, we show that anomaly constraints…
One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to…
The Coupled Cluster (CC) and full CI expansions are studied for three fermions with six and seven modes. Surprisingly the CC expansion is tailor made to characterize the usual SLOCC entanglement classes. It means that the notion of a SLOCC…
In this paper, the basis states of the minimal left ideals of the complex Clifford algebra $C\ell(8)$ are shown to contain three generations of Standard Model fermion states, with full Lorentzian, right and left chiral, weak isospin, spin,…
Topological order in two dimensions can be described in terms of deconfined quasiparticle excitations - anyons - and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation…