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A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A…
Generalized parton distribution functions (GPDs) of spin-3/2 particles are defined for the first time in this paper. Eight unpolarized and eight polarized GPDs are found. In the forward limit of GPDs, the structure functions and parton…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the…
We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…
In the present article we calculate the expectation values of of S$_{z}$ and S$^{2}$ operators for spin-1 and spin-3/2 particles by expanding a general wave function which includes all spin values. The results are same as in the stantard…
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
Many Generalized Uncertainty Principle (GUP) models modify the inner-product measure to ensure symmetric position or momentum operators. We show that an alternate approach to these GUPs is to symmetrize the operators rather than modifying…
We extend the counting of generalized form factors presented in PRD63(2000) by Ji and Lebed to the axial vector and the tensor operator at twist-2 level. Following this, a parameterization of all higher moments in x of the tensor (helicity…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
In this paper we extend our previous result on the description of the partcle motion in a generalized Heisenberg picture to a relativistic fermion. The operators of the Lorentz algebra in this picture may be regarded as field operators. In…
Time-resolved Faraday rotation measurements have proved transformative in the investigation of spin dynamics in semiconductors. In materials with spin lifetimes which are on the order of, or greater than, the laser repetition time, the…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
In polarimetry, a superposition of internal quantal states is exposed to a single Hamiltonian and information about the evolution of the quantal states is inferred from projection measurements on the final superposition. In this framework,…
Positive operator valued measures (POVMs) are presented that allow an unknown pure state of a spin-1 particle to be determined with optimal fidelity when 2 to 5 copies of that state are available. Optimal POVMs are also presented for a…
In a neutron polarimetry experiment the mixed state relative phases between spin eigenstates are determined from the maxima and minima of measured intensity oscillations. We consider evolutions leading to purely geometric, purely dynamical…
We define a new operator within Barnett-Pegg formalism for phase angle. The physical predictions for this operator correspond to those expected of an angular velocity operator. Examples studied are particle on a circle with and without…
We consider a class of generalised single mode Dicke Hamiltonians with arbitrary boson coupling in the pseudo-spin $x$-$z$ plane. We find exact solutions in the thermodynamic, large-spin limit as a function of the coupling angle, which…
In this paper we present a state vector analysis of the generation of atomic spin squeezing by measurement of an optical phase shift. The frequency resolution is improved when a spin squeezed sample is used for spectroscopy in place of an…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…