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A superstring action is quantised with Neveu–Schwarz (NS) and Ramond (R) boundary conditions. The zero mass states of the NS sector are classified as the vector gluons, W-mesons, B_μ-mesons and scalars containing Higgs. 15 zero mass fermions are obtained from the Ramond sector. A spacetime supersymmetric Hamiltonian of the Standard Model is presented without any conventional SUSY particles.

We investigate the charged particle spectra produced in the heavy-ion collisions at nine centralities from different systems, i.e. $\mathrm{\text{Pb}}+\mathrm{\text{Pb}}$ at $\sqrt{s_{NN}}=2.76$ TeV and 5.02 TeV as well as $\mathrm{\text{Xe}}+\mathrm{\text{Xe}}$ at $\sqrt{s_{NN}}=5.44$ TeV, at Large Hadron Collider (LHC) using one empirical formula inspired by the stationary solution of the Fokker-Planck equation, dubbed as the generalized Fokker-Planck solution (GFPS). Our results show that the GFPS can reproduce the experimental particle spectrum up to transverse momentum $p_T$ about 45 GeV/c with the maximum discrepancy 30% covering 10 orders of magnitude. The discrepancy between the data and the results from the GFPS decreases to 15% when the maximum of the charged particle transverse momentum is cut to 20 GeV/c. We confirmed that the Tsallis distribution derived from the non-extensive statistics, which can reproduce the particle spectra produced in small collision systems, such as $\mathrm{\text{p}}+\mathrm{\text{p}}$, up to few hundreds GeV/c, can only apply to systematically study the particle spectra up to 8 GeV/c in $\mathrm{\text{A}}+\mathrm{\text{A}}$ collisions at LHC, as pointed out in the study of identified particle spectra in $\mathrm{\text{Pb}}+\mathrm{\text{Pb}}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV. A brief discussion on GFPS is also given.

The classical sine–Gordon model is a two-dimensional integrable field theory, with particle-like solutions — the so-called solitons. Using its integrability one can define the quantum theory without the process of canonical quantization. The bootstrap method employs the fundamental properties of the model to restrict the structure of the scattering matrix as far as possible. The classical model can be extended with integrable discontinuities, purely transmitting jump defects. Then the quantum version of the extended model can be determined via the bootstrap method again. The resulting quantum theory contains the so-called CDD uncertainty. The aim of this article is to carry out the semiclassical approximation on both the classical and the quantum side of the defect sine–Gordon theory. The CDD ambiguity can be restricted by comparing the two results. To complete the comparison we have to calculate the relation between the classical and quantum parameters. We determine the quantum parameters from the poles of the T matrix, and we find that there are resonances in the spectrum.

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the classification group $\mathrm{\text{SU}}(3)\times \mathrm{\text{SU}}{(2)}_L\times \mathrm{\text{SU}}{(2)}_R$, which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge $-4/3$ and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain $4{sin}^2{𝜃}_w=1-2\alpha /3{\alpha }_s$ which is not far from the experimental value around the $M_Z$ mass.