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We draw attention on the procedure, where Standard Model predictions and experimental results are compared and certain new physics scenarios are ruled out, that requires great attention, since there is still a room for new physics,…
In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley…
A new set of projection operators for three-dimensional models are constructed. Using these operators, an uncomplicated and easily handling algorithm for analysing the unitarity of the aforementioned systems is built up. Interestingly…
This work deals with the measurability of Fourier integral operators (FIOs) with random phase and amplitude functions. The key ingredient is the proof that FIOs depend continuously on their phase and amplitude functions, taken from suitable…
In this article, we extend the %Weyl-van der Waerden spinor technique for calculating helicity amplitudes to general massive fields of half-integer spins. We find that the little group generators can be represented as first-order…
We study the longitudinal spin polarization of a relativistic fluid of massive spin-1/2 particles undergoing a boost-invariant expansion in the longitudinal direction and rotating in the transverse plane. We express the polarization vector…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
Polarization measurements provide a detailed method to test the Standard Model and to search for new physics. Most previous studies depend on pre-selected coordinates, which blurs the significance of the results. The construction of two…
The generalized parton distributions (GPDs) for the spin-3/2 $\Delta^+$ resonance are studied numerically by using a diquark spectator approach. Our results show that symmetric constraints from time reversal on GPDs are satisfied. The axial…
The quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field is analyzed for the general case where scalar and vector couplings are considered. The energy spectra are explicitly computed for different physical…
We study the phase diagram of one dimensional spin one-half fermionic cold atoms. The two ``spin'' species can have different hopping or mass. The phase diagram at equal densities of the species is found to be very rich, Mott insulators as…
It has been shown recently that additional information can be obtained from charged particle multiplicity distribution by investigating their modified combinants $C_j$, which exhibit periodic oscillatory behaviour. The modified combinants…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
The geometric phase is usually treated as a quantity modulo 2\pi, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present…
This paper sets out to establish a comparative study between classes of spin- and velocity-dependent potentials for spin-1/2 and spin-1 matter currents/sources in the non-relativistic regime. Both (neutral massive) scalar and vector…
The behavior of the geometric phase gained by a single spin-1/2 nucleus immersed into a thermal or a squeezed environment is investigated. Both the time dependence of the phase and its value at infinity are examined against several physical…
We elaborate on the traceless and transverse spin projectors in four-dimensional de Sitter and anti-de Sitter spaces. The poles of these projectors are shown to correspond to partially massless fields. We also obtain a factorisation of the…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…