Related papers: Helicity Basis and Parity
We study the theory of the Lorentz group (1/2,0)+(0,1/2) representation in the helicity basis of the corresponding 4-spinors. As Berestetski, Lifshitz and Pitaevskii mentioned, the helicity eigenstates are not the parity eigenstates.…
We study the theory of the (1/2,0)+(0,1/2) and (1,0)+(0,1) representations in the helicity basis. The helicity eigenstates are not the parity eigenstates. This is in accordance with the idea of Berestetskii, Lifshitz and Pitaevskii. The…
We study the theory of the (1/2,0)+(0,1/2) and (1,0)+(0,1) representations of the Lorentz group in the helicity basis. The helicity eigenstates are not the parity eigenstates. This is in accordance with the idea of Berestetskii, Lifshitz…
We write solutions of relativistic quantum equations explicitly in the helicity basis for S=1/2 and S=1. We present the analyses of relations between Dirac-like and Majorana-like field operators. Several interesting features of bradyonic…
We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that…
It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
In this essay, an {\it ab initio} study of the self/anti-self charge conjugate $(1/2,\,0)\oplus(0,\,1/2)$ representation space is presented. Incompatibility of self/anti-self charge conjugation with helicity eigenstates and gauge…
Spin 1 particle is investigated in 3-dimensional curved space of constant negative curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin--Kemmer equation in quasi…
An extension of the scope of quantum theory is proposed in a way inspired by the recent heuristic as well as phenomenological success of the use of non-Hermitian Hamiltonians which are merely required self-adjoint in a Krein space with an…
By considering the parity-transformation properties of the $(1/2,\,0)$ and $(0,\,1/2)$ fields in the {\it front form} we find ourselves forced to study the front-form evolution both along $x^+$ and $x^-$ directions. As a by product, we find…
We study the discrete symmetries (P,C and T) on the kinematical level within the extended Poincare Group. On the basis of the Silagadze research, we investigate the question of the definitions of the discrete symmetry operators both on the…
We calculate the helicity and chirality effects experienced by a spin-1/2 particle subjected to classical electromagnetic and gravitational fields. The helicity evolution is then determined in the non-relativistic, relativistic, and…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
Lorentz transformation of the reduced helicity density matrix for a massive spin 1/2 particle is investigated in the framework of relativistic quantum information theory for the first time. The corresponding helicity entropy is calculated,…
We show that under the operation of parity the {\it front-form} $(1/2,\,0)$ and $(0,\,1/2)$ Weyl spinors (massive or massless) do not get interchanged. This has the important consequence that if a front-form theory containing…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
Some PT-symmetric non-hermitean Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
In $D=2+1$ dimensions there are two dual descriptions of parity singlets of helicity $\pm 1$, namely the self-dual model of first-order (in derivatives) and the Maxwell-Chern-Simons theory of second-order. Correspondingly, for helicity $\pm…