C-P-T Fractionalization

The purposes of this paper is to investigate the properties of the quantum extended strange superalgebra $\tilde{P}_{Q}(n)$ when his deformation parameter $Q$ goes to a root of unity.

The motivations for the construction of an 8-component representation of fermion fields based on a two dimensional representation of time reversal transformation and CPT invariance are discussed. Some of the elementary properties of the quantum field theory in the 8-component representation are studied. It includes the space-time and charge conjugation symmetries, the implementation of a reality condition, the construction of interaction theories, the field theoretical imagin...

These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a path-integral viewpoint. The group-theoretical underpinnings of relativistic fractional spin are discussed, then the path-integral quantization of spin and of massive fermions without using spinors is reviewed. The path integral for a system of n relat...

We describe a novel class of quantum mechanical particle oscillations in both relativistic and nonrelativistic systems based on $PT$ symmetry and $T^2=-1$, where $P$ is parity and $T$ is time reversal. The Hamiltonians are chosen at the outset to be self-adjoint with respect to a PT inner product. The quantum mechanical time evolution is based on a modified CPT inner product constructed in terms of a suitable C operator. The resulting quantum mechanical evolution is shown to ...

After analyzing the implication of investigations on the C, P and T transformations since 1956, we propose that there is a basic symmetry in particle physics. The combined space-time inversion is equivalent to particle-antiparticle transformation, denoted by ${\cal PT=C}$. It is shown that the relativistic quantum mechanics and quantum field theory do contain this invariance explicitly or implicitly. In particular, (a) the appearance of negative energy or negative probability...

Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered example is a type of subsystem symmetry fractionalization that occurs through a different mechanism to global symmetry fractionalization. In this work we extend the study of subsystem symmetry fractionalization through new examples derived...

We investigate the intrinsic reason for spin statistics connection. It is found that if a free field theory is rotationally (SU(2)) invariant, and has time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin statistics connection, except for a special case. Shr{\"o}dinger equation belongs to this special case, and does not obey spin statistics connection. Further we show that if the energy spectrum of a particle $E(p)$ takes the form of a square root, na...

We study the non relativistic limit of the charge conjugation operation $\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\cal C$, $\cal P$ (parity) and $\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Al...

This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative approach to QFT for combining the quantum mechanics and special theory of relativity which keeps the concept of wave function (belonging to some representation of Lorentz group) through the whole theory. Scalar product has been redefined to take ...

EPR experiment on $K^0-\bar{K}^0$ system in 1998\cite{1} strongly hints that one should use operators $\hat{E}_c=-i\hbar\frac{\partial}{\partial t}$ and $\hat{\bf p}_c=i\hbar\nabla$ for the wavefunction (WF) of antiparticle. Further analysis on Klein-Gordon (KG) equation reveals that there is a discrete symmetry hiding in relativistic quantum mechanics (RQM) that ${\cal P}{\cal T}={\cal C}$. Here ${\cal P}{\cal T}$ means the (newly defined) combined space-time inversion (with...