Spin-1 Bosons Research Articles

Duality-invariant superconformal higher-spin models

We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics developed by Gaillard and Zumino, Gibbons and Rasheed, and generalised by Ivanov and Zupnik. For each integer spin $s\geq 2$ we demonstrate the existence of families of conformal $\mathsf{U}(1)$ duality-invariant models, including a generalisation of the so called ModMax Electrodynamics ($s=1$). Our bosonic results are then extended to the $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric cases. We also sketch a formalism of duality rotations for conformal gauge fields of Lorentz type $(m/2, n/2)$, for positive integers $m $ and $n$.

Spinorial Snyder and Yang models from superalgebras and noncommutative quantum superspaces

The relativistic Lorentz-covariant quantum space-times obtained by Snyder can be described by the coset generators of (anti) de-Sitter algebras. Similarly, the Lorentz-covariant quantum phase spaces introduced by Yang, which contain additionally quantum curved fourmomenta and quantum-deformed relativistic Heisenberg algebra, can be defined by suitably chosen coset generators of conformal algebras. We extend such algebraic construction to the respective superalgebras, which provide quantum Lorentz-covariant superspaces (SUSY Snyder model) and indicate also how to obtain the quantum relativistic phase superspaces (SUSY Yang model). In last Section we recall briefly other ways of deriving quantum phase (super)spaces and we compare the spinorial Snyder type models defining bosonic or fermionic quantum-deformed spinors.

Bulk plasmaritons: Wave-mechanical and second-quantized theories

Inspired by a recently established quantum theory for bulk and surface plasmons [Jung and Keller, Phys. Rev. A 103, 063501 (2021).], wave-mechanical and second-quantized quantum electrodynamic theories for bulk plasmaritons in a homogeneous jellium are presented. Starting from the ``inner'' structure of the transversely polarized classical plasmariton mode, it is argued that a plasmariton quasiparticle may be formed by an always attached pair consisting of a transverse (gauge) photon and a never observable transverse plasmon. A first-quantized plasmariton theory is established from a plasmariton Klein-Gordon equation. It is shown that the plasmariton can be perceived as a diamagnetically driven spin-1 boson quasiparticle. A Lagrangian-Hamiltonian formalism is used to extend the first-quantized plasmariton theory to the second-quantized level. The minimal coupling principle is used to change the free QED theory into a theory coupling the plasmariton to an electromagnetic gauge field. Using the microscopic transverse Lindhard (random phase approximation) dielectric function, it is shown that for small wave numbers, the classical Boltzmann equation part of the Lindhard dielectric function results in a hydrodynamic Brewster branch, the quantization of which follows that of a vectorial Klein-Gordon equation. For plasmariton wave numbers larger than the Fermi wave number, a pure electrostatic model (with no magnetic-field component) results in a harmonic-oscillator description of the plasmariton's polarization field. With inspiration and elements from the Power-Zinau-Wolley description, the Pauli-Fierz theory for particle-tied transverse photons, and the propagator theory of Keller for the spatial localization of transverse photons, a formalism in which the plasmariton quasiparticle is dressed by a cloud of transverse (long-wavelength) photons is developed. The quantized radiated part of the electromagnetic field is described by a free-field quantization of the transverse part of the displacement field (${\mathbf{D}}_{T}$). The total Hamiltonian is diagonalized, and the resulting dispersion relation obtained. The interaction between the transverse radiated and attached photons implies that a strongly localized and charged plasmariton quasiparticle with its tied photons vibrates as a simple harmonic oscillator in the ``external'' radiative transverse photon field.

Speeding up quantum dissipative dynamics of open systems with kernel methods

The future forecasting ability of machine learning (ML) makes ML a promising tool for predicting long-time quantum dissipative dynamics of open systems. In this article, we employ nonparametric ML algorithm (kernel ridge regression as a representative of the kernel methods) to study the quantum dissipative dynamics of the widely-used spin-boson (SB) model. Our ML model takes short-time dynamics as an input and is used for fast propagation of the long-time dynamics, greatly reducing the computational effort in comparison with the traditional approaches. Presented results show that the ML model performs well in both symmetric and asymmetric SB models. Our approach is not limited to SB model and can be extended to complex systems.

Quantum Lifshitz transitions generated by order from quantum disorder in strongly correlated Rashba spin-orbit-coupled systems

We study the system of strongly interacting spinor bosons in a square lattice subject to the isotropic Rashba spin-orbit coupling $\ensuremath{\alpha}=\ensuremath{\beta}$. It supports a collinear spin-bond correlated magnetic Y-x phase, a gapped coplanar in-commensurate (IC) XY-y phase, and a noncoplanar commensurate (C) $3\ifmmode\times\else\texttimes\fi{}3$ Skyrmion crystal phase. The state at the Abelian point $\ensuremath{\alpha}=\ensuremath{\beta}=\ensuremath{\pi}/2$ is just a ferromagnetic state in a rotated basis. Slightly away from the point, we identify a spurious $\text{U}(1)$ symmetry, develop a nonperturbative method to calculate not only the gap but also the excitation spectrum due to the order from quantum disorder (OFQD) mechanism. We construct a symmetry-based effective action to investigate the quantum Lifshitz transition from the Y-x state to the IC XY-y state and establish the connection between the phenomenological parameters in the effective action and those evaluated by the microscopic nonperturbative OFQD analysis in the large $S$ limits. Experimental implications on cold atoms and some $4d$ or $5d$ Kitaev materials are discussed.

Mass, Spin, and Ultralight Boson Constraints from the Intermediate-mass Black Hole in the Tidal Disruption Event 3XMM J215022.4–055108

Abstract We simultaneously and successfully fit the multiepoch X-ray spectra of the tidal disruption event (TDE) 3XMM J215022.4−055108 using a modified version of our relativistic slim disk model that now accounts for angular momentum losses from radiation. We explore the effects of different disk properties and of uncertainties in the spectral hardening factor f c and redshift z on the estimation of the black hole mass M • and spin a •. Across all choices of theoretical priors, we constrain M • to less than 2.2 × 104 M ⊙ at 1σ confidence. Assuming that the TDE host is a star cluster associated with the adjacent, brighter, barred lenticular galaxy at z = 0.055, we constrain M • and a • to be 1.75 − 0.05 + 0.45 × 10 4 M ⊙ and 0.8 − 0.02 + 0.12 , respectively, at 1σ confidence. The high, but sub-extremal, spin suggests that, if this intermediate-mass black hole (IMBH) has grown significantly since formation, it has acquired its last e-fold in mass in a way incompatible with both the “standard” and “chaotic” limits of gas accretion. Ours is the first clear IMBH with a spin measurement. As such, this object represents a novel laboratory for astroparticle physics; its M • and a • place tight limits on the existence of ultralight bosons, ruling out those with masses from ∼10−15 to 10−16 eV.

Z′-explorer: A simple tool to probe Z′ models against LHC data

New Physics model building requires a vast number of cross-checks against available experimental results. In particular, new neutral, colorless, spin-1 bosons Z′, can be found in many models. We introduce in this work a new easy-to-use software Z′-explorer which probes Z′ models to all available decay channels at LHC. This program scrutinizes the parameter space of the model to determine which part is still allowed, which is to be shortly explored, and which channel is the most sensitive in each region of parameter space. The user does not need to implement the model nor run any Monte Carlo simulation, but instead just needs to use the Z′ mass and its couplings to Standard Model particles. We describe Z′-explorer backend and provide instructions to use it from its frontend while applying it to a variety of Z′ models. In particular, we show Z′-explorer application and utility in a sequential Standard Model, a B-L Z′ and a simplified two-sector or Warped/Composite model. The output of the program condenses the phenomenology of the model features, the experimental techniques, and the search strategies in each channel in an enriching outcome. We find that compelling add-ons to the software would be to include correlation between decay channels, low-energy physics results, and Dark Matter searches. The software is open-source ready to use, and available for modifications, improvements, and updates by the community. Program summaryProgram Title::Z′-explorerCPC Library link to program files:https://doi.org/10.17632/k7tdp8kwgf.1Developer's repository link:github.com/ro-sanda/Z--explorerLicensing provisions: GNU General Public License v3Programming language: C++ and bashNature of problem: Many New Physics models have a Z' in its spectrum. As any new model, it should be contrasted to experimental results in all its predictions. In particular, if they have a Z', there are many constraints that should be satisfied simultaneously. Also, one may wonder which of all these constraints –if satisfied– would be the optimal channel to look for the Z' in the proposed New Physics model.Solution method: The Z'-explorer software makes a fast and practical answer to both problems: i) Whether a Z' is discarded or not by experimental results, and ii) Which is the most sensitive channel to look for it. Being very easy to implement, the Z'-explorer tool allows to test a New Physics Z' against all the LHC direct observables of Z' searches, and provides the sensitivity to each one of them.

On Existence of Ground States in the Spin Boson Model

We show the existence of ground states in the massless spin boson model without any infrared regularization. Our proof is non-perturbative and relies on a compactness argument. It works for arbitrary values of the coupling constant under the hypothesis that the second derivative of the ground state energy as a function of a constant external magnetic field is bounded.

Realization of a bosonic antiferromagnet

Quantum antiferromagnets are of broad interest in condensed matter physics as they provide a platform for studying exotic many-body states including spin liquids and high-temperature superconductors. Here, we report on the creation of a one-dimensional Heisenberg antiferromagnet with ultracold bosons. In a two-component Bose-Hubbard system, we switch the sign of the spin-exchange interaction and realize the isotropic antiferromagnetic Heisenberg model in an extended 70-site chain. Starting from a low-entropy N\'eel-ordered state, we use optimized adiabatic passage to approach the bosonic antiferromagnet. We demonstrate the establishment of antiferromagnetism by probing the evolution of the staggered magnetization and spin correlations of the system. Compared with condensed matter systems, ultracold gases in optical lattices can be microscopically engineered and measured, offering significant advantages for exploring bosonic magnetism and spin dynamics.

Symmetry-protected topological phases in spinful bosons with a flat band

We theoretically demonstrate that interacting symmetry-protected topological (SPT) phases can be realized with ultracold spinful bosonic atoms loaded on the lattices which have a flat band at the bottom of the band structure. Ground states of such systems are not conventional Mott insulators in the sense that the ground states possess not only spin fluctuations but also non-negligible charge fluctuations. The SPT phases in such systems are determined by both spin and charge fluctuations at zero temperature. We find that the many-body ground states of such systems can be exactly obtained in some special cases, and these exact ground states turn out to serve as representative states of the SPT phases. As a concrete example, we demonstrate that spin-1 bosons on a sawtooth chain can be in an SPT phase protected by $\mathbb{Z}_2 \times \mathbb{Z}_2$ spin rotation symmetry or time-reversal symmetry, and this SPT phase is a result of spin fluctuations. We also show that spin-3 bosons on a kagome lattice can be in an SPT phase protected by $D_2$ point group symmetry, but this SPT phase is, however, a result of charge fluctuations.

Higher spin dark matter

Little is known about dark matter beyond the fact that it does not interact with the standard model or itself, or else does so incredibly weakly. A natural candidate, given the history of no-go theorems against their interactions, are higher spin fields. Here we develop the scenario of higher spin (spin s>2) dark matter. We show that the gravitational production of superheavy bosonic higher spin fields during inflation can provide all the dark matter we observe today. We consider the observable signatures, and find a potential characteristic signature of bosonic higher spin dark matter in directional direct detection; we find that there are distinct spin-dependent contributions to the double differential recoil rate, which complement the oscillatory imprint of higher spin fields in the cosmic microwave background. We consider the extension to higher spin fermions and supersymmetric higher spins.

Enhancing Associative Memory Recall and Storage Capacity Using Confocal Cavity QED

We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the cavity modes serving as the synapses, connecting a network of superradiant atomic spin ensembles, which serve as the neurons. Memories are encoded in the connectivity matrix between the spins, and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin-glass regime as a physical parameter is tuned---the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics, rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network's ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.

Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation.

In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion. Introducing transformed SPFs, which obey normalization conditions typically associated with SHFs, revised equations of motion are derived. These equations do not show the singularities resulting from the inverse single-particle density matrix and are invariant under tree transformations. Based on the revised equations of motion, a new integration scheme is introduced. The scheme combines the advantages of the constant mean-field approach of Beck and Meyer [Z. Phys. D 42, 113 (1997)] and the singularity-free integrator suggested by Lubich [Appl. Math. Res. Express 2015, 311]. Numerical calculations studying the spin boson model in high dimensionality confirm the favorable properties of the new integration scheme.

Cubic vertices for [formula omitted] supersymmetric massless higher spin fields in various dimensions

Using the BRST approach to higher spin field theories we develop a generic technique for constructing the cubic interaction vertices for N=1 supersymmetric massless higher spin fields on four, six and ten dimensional flat backgrounds. Such an approach allows formulation of the equations for cubic vertices including bosonic and fermionic higher spin fields, and the problem of finding the vertices is reduced to finding the consistent solutions to these equations. As a realization of this procedure, we present the particular solutions for the vertices where the fields obey some off-shell constraints. It is shown that the supersymmetry imposes additional constraints on the vertices and singles out a particular subclass of the solutions. As a concrete application of the generic scheme, we consider supersymmetric Yang-Mills-like systems in four, six and ten dimensions where the higher spin fields transform under some internal symmetry group, as well as supergravity-like systems in the same dimensions.

Stability of supercurrents in a superfluid phase of spin-1 bosons in an optical lattice

We study collective modes and superfluidity of spin-1 bosons with antiferromagnetic interactions in an optical lattice based on the time-dependent Ginzburg-Landau (TDGL) equation derived from the spin-1 Bose-Hubbard model. Specifically, we examine the stability of supercurrents in the polar phase in the vicinity of the Mott insulating phase with even filling factors. Solving the linearized TDGL equation, we obtain gapless spin-nematic modes and gapful spin-wave modes in the polar phase that arise due to the breaking of $S^2$ symmetry in spin space. Supercurrents exhibit dynamical instabilities induced by growing collective modes. In contrast to the second-order phase transition, the critical momentum of mass currents is finite at the phase boundary of the first-order superfluid-Mott insulator (SF-MI) phase transition. Furthermore, the critical momentum remains finite throughout the metastable SF phase and approaches zero towards the phase boundary, at which the metastable SF state disappears. We also study the stability of spin currents motivated by recent experiments for spinor gases. The critical momentum of spin currents is found to be zero, where a spin-nematic mode causes the dynamical instability. We investigate the origin of the zero critical momentum of spin currents and find it attributed to the fact that the polar state becomes energetically unstable even in the presence of an infinitesimal spin current. We discuss implications of the zero critical momentum of spin currents for the stability of the polar state.

КОМПОНЕНТ ТЕМНОЇ МАТЕРІЇ І СОНЦЕ

Some consequences from the hypothesis of the origin of particles of one of the components of dark matter are presented. The reason for the hypothesis was the observational data of stellar radiation, considered through the prism of the relationship of all phenomena in Nature and the law of conservation of energy. It is argued that a part of the stellar electromagnetic radiation, which does not participate in the interaction with baryonic matter, will not wander forever in space. This radiation will interact with a subtle level of matter, continuously giving it its energy, shifting to the microwave region. In this frequency region, two quanta of close energies can form a neutral boson of spin 0, or spin 2, on opposite “courses”. Based on the observed spectrum of cosmic microwave radiation, it is assumed that these Bose particles have a continuous mass spectrum. These light nonrelativistic bosons are precisely the component of the thin medium that interacts with stellar radiation, taking energy from it. Bose particles participate in gravitational interactions. This means that in addition to the distribution of dark matter around galaxies, an increased concentration of particles in the form of large clouds can be observed in it. If an internal shock wave appears in such a cloud, located far from galactic streams of baryon particles, it will destroy the particles of the cloud, creating “strange radio circles” visible exclusively in the radio range. The gravitational interaction causes dark particles to drift towards large clusters of visible matter. The process of their drift to massive objects will be accompanied by resistance from the outgoing stellar radiation. Therefore, near the surface of a burning star, these particles themselves will resist the outgoing radiation, shifting it towards longer wavelengths. The plasma ejected by the star, with sufficient energy of its particles, is capable of destroying the particles of the dark component, creating pairs of photons and providing itself with "seed" quanta for bremsstrahlung. Free quanta remaining from the decay of dark particles will give microwave radiation. Therefore, burning stars should exhibit a redshift in the emission spectra and microwave radiation. Taking a certain model in the distribution of the dark component of matter near the Sun, it is possible to predict the nature of the redshift in the spectra of its radiation as the observation point moves along the solar disk from its center to the limb. A similar conclusion is made regarding the intensity of microwave radiation near the surface of the star. The galactic movement of the Sun should lead to some temperature effects associated with a denser counter flow of dark particles to the corresponding area of the solar surface. Knowing the direction of motion of the Sun in the Galaxy, based on the results of the temperature deviation on the surface of the star, one can determine the local speed and direction of movement of the cloud of the dark component of matter.

Theory of 3F4D Universe (Beyond Standard Model of Particle Physics)

In this theory, “mass is equivalent to length of imaginary straight line segment” and “direction to imaginary line segment is intrinsic property of that particle which is Equivalent to its intrinsic spin”. With this concept, all fundamental particles, fermions and bosons are described as quanta imaginary string particles with a definite direction. For e.g. unidirectional imaginary straight line with fixed length are massive spin 1/2 fermions; while unidirectional imaginary quanta curved lines are massless spin 1 bosons. Thus, it gives co-relation between massless (curved imaginary line) and spin = 1 properties of boson as proved in QED theory. All fundamental particles of standard model and beyond standard model are arranged in one simple diagram in 3 folds (bottom fold, middle upper and lower folds and top fold) and are projected in 4th Imaginary Dimension in order of decreased in Mass from TeV to approx. 0 eV. This theory is beyond standard model because it predicts new fundamental particles viz. dark matter (spin = 0 massive boson) along with gravitons (spin = 2, massless bosons); 4th pair of neutrinos, vertical massless boson (VMB) particles and tri-axis massive boson (spin = 0) particle. The discovery of these new particles will act as solid proof to this theory. With this 3F4D representation of the universe at an atomic and sub-atomic level, it solves lots of current problems of SM of particle physics like matter-antimatter asymmetry, origin of mass of hadrons like protons, origin of mass and L.H. nature for neutrinos, wave-particle duality of particles, etc. giving true insight of fundamental particles. With proving that, dark matter is not a quanta particle, rather it is a single entity and spreads/expands throughout the universe in the form of “web of spider”, it shows space-time is not empty, but it is filled with Continuous lines of Dark Matter and we, materialistic massive objects are floating/sailing w.r.t. current of this vast ocean. Correlation of its continuity with time gives new a definition to time: “Time is neither Illusion nor 4th Dimension, but, it represents Continuous Flow of Single Entity, Dark Matter”. Space-time is not Empty and is filled with massive dark matter, hence, we have to add more terms to newtonian gravitational equation to account for gravitational strength of mass of surrounding dark matter which represents curvature of space-time in terms of Increase in its mass-density w.r.t. to mass-density of flat universe. Finally, using an empirical formula (h = k*c*Q; k = boltzmann’s constant = mass in TeV range) and inverse relation of mass-density of DM with age of the universe (H2 = Constant&#8226G&#8226Mass-Density of DM); Unification of Gravity at TeV is achieved without consideration of “Gravitational Constant, G”, hence, Planck’s Scale is not required.

Cluster mean-field study of spinor Bose–Hubbard ladder: Ground-state phase diagram and many-body population dynamics* *Project supported by the Key-Area Research and Development Program of GuangDong Province, China (Grant No. 2019B030330001), the National Natural Science Foundation of China (Grant Nos. 11874434 and 11574405), the Science and Technology Program of Guangzhou, China (Grant No. 201904020024), and the Guangzhou Science and Technology Projects

We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose–Hubbard ladder (BHL). For unbiased BHL, we find superfluid (SF) phase and integer filling Mott insulator (IntMI) phase. For biased BHL, in addition to the SF and IntMI phases, there appears half-integer filling Mott insulator (HIntMI) phase. The phase transition between the SF and IntMI phases can be first order at a part of phase boundaries, while the phase transition between the SF and HIntMI phases is always second order. By tuning the bias energy, we report on the change of the nature of SF–MI phase transitions. Furthermore, we study the effect of the spin-dependent interaction on the many-body population dynamics. The spin-dependent interaction can lead to rich dynamical behaviors, but does not influence the particle transfer efficiency. Our results indicate a way to tune the nature of the SF–MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

The Pauli Exclusion Principle and the Problems of its Theoretical Substantiation1

The modern state of the Pauli Exclusion Principle (PEP) is discussed. PEP can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is the so-called spin-statistics connection (SSC). As we will discuss, the physical reasons why SSC exists are still unknown. On the other hand, according to PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, both belong to one-dimensional representations of the permutation group, all other types of permutation symmetry are forbidden; whereas the solution of the Schrodinger equation may have any permutation symmetry. It is demonstrated that the proof in some textbooks on quantum mechanics that only symmetric and antisymmetric states can exist is wrong. However, the scenarios, in which arbitrary permutation symmetry (degenerate permutation states) is permitted, lead to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature of particles only in nondegenerate permutation states (symmetric and antisymmetric) is not accidental and so-called symmetrization postulate should not be considered as a postulate, since all other symmetry options for the total wave function may not be realized. From this an important conclusion follows: we may not expect that in the future some unknown elementary particles can be discovered that are not fermions or bosons.