We report on our current and past activities on the development of a training and teaching program for primary schools devoted to the
Standard Model of Particle Physics. The project has been held in several schools in Bergamo area (northern Italy), based on the
original Particle Physics for Primary Schools format proposed by C.Lazzeroni at the University of Birmingham (UK) (2017-present).
The program is fostered by a joint collaboration between INFN - Milano Bicocca, the primary school IC Carvico and the University of Birmingham.
The outcomes suggest that a wide interest exists both in teachers and in students and their families about cutting-edge science.
Being passionate about science can be an inspiring attitude for young people and children, especially when they will choose their future academic
and professional path. The program also aims at removing the gender bias and some deeply rooted common misbeliefs about science.
The importance of a prospective stable institutional mechanism to train teachers on the latest results in science as well as of an
enduring cooperation on pedagogical transposition of science achievements is emphasized. We also mention several possible directions in order to further expand our current activities by stressing the links with specific skills and competences that match the curriculum in both primary and secondary schools.

We developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) [1]. The proposed approach combines and expands the approaches of algebraic quantum field theory [2] and theory of algebraic spinors [3]. It is based on the use of Grassmann densities in the momentum space and derivatives with respect to them [4-5] and the construction from these densities of both basic Clifford vectors of spacetime and spinor vacuum [5].

P, C, and T transformations are defined as operators that change basis Clifford vectors, but do not change components of spinors and vectors. We have shown that, with this approach, C and T are Clifford complex conjugation and Clifford transposition operators invariant to the choice of matrix or other linear representation of the Clifford group. And that they can be exact symmetries only in phenomena in which tensor quantities appear or in those where only spinors or only conjugated spinors are involved. A symmetry operator iQ also exists for electrically charged spinors. It is a reflection operator of two basic Clifford vectors corresponding to the internal degrees of freedom of spinors.

We have shown that P, CT, iQ, and CTP can be exact symmetries of spinors, and that CTP is a generalized Dirac conjugation [4] operator.

1. Gårding L., Wightman A. Proc. Nat. Acad. Sci. USA, 1954, v. 40, p. 617.
2. Haag R., Kastler D. Journal of Mathematical Physics, 1964, v. 5, p. 848.
3. Lounesto P. Clifford algebras and spinors. Cambridge University Press, 2001.
4. Monakhov V. V. Theoretical and Mathematical Physics, 2019, v. 200, p. 1026.
5. Monakhov V. Universe, 2019, v. 5, p. 162.

Quantum electrodynamics (QED) and the electroweak theory are very successful in explaining quantum phenomena for electromagnetic and weak interactions. Their predictions agree with experimental data to great precision. Attempts to use this technique for strong interactions do not lead to a full success. This suggests that at present we do not clearly understand the nature of quantization. It is reasonable to assume that there should exist some well-defined mathematical procedure of quantization which can be applied to any field theory.

Taking all this into account, it is of great interest to construct nonperturbative QED for some simple case in order to compare perturbative and nonperturbative QED. It would allow one to understand the physical essence of such phenomena like the renormalization, convergence of the Feynman integral, etc. One can assume that such a possibility may arise in constructing QED on some compact manifold, since in this case spectra of eigenvalues of the Dirac and Maxwell equations will presumably be discrete. Here we suggest a scheme of nonperturbative quantization of coupled Dirac and Maxwell fields on the Hopf bundle.

The most important part of our study is the procedure of nonperturbative quantization suggested for the interacting Dirac and Maxwell fields. Following Heisenberg, we have replaced the classical equations by equations for operators of the corresponding fields. Since the operator equation can scarcely be solved somehow, it is replaced by an infinite set of equations for Green's functions.

To illustrate the suggested scheme of nonperturbative quantization, we have considered some physical system possessing perfectly definite Ansatze for the spinor and electromagnetic fields. This gives the much simpler set of equations, for which we have written out the first few equations for 1- and 2-point Green's functions.

Monopole solutions in SU(2) Yang-Mills theory which interact with massive nonlinear spinor fields described by the nonlinear Dirac equation are obtained. These solutions describe a magnetic monopole created by a spherical lump of nonlinear spinor fields.

It is shown that the monopole solutions obtained differs in principle from the ’t Hooft-Polyakov monopole so that its: (а) topologically trivial; (b) the radial magnetic field of which decreases as r^-3 ; (c) for its existence no need the Higgs field.

It is demonstrated that the energy spectrum of such a system possesses a global minimum, the appearance of which is due exclusively to the nonlinearity of the Dirac spinor fields. This global minimum can be considered as a mass gap, i.e. the energy difference between a vacuum and the next lowest energy state. A similar minimum was found for the energy spectrum of regular solutions to the nonlinear Dirac equation and this minimun called as “the lightest stable particle”.

References

1. Dzhunushaliev, V. Folomeev, and A. Makhmudov, “Non-Abelian Proca-Dirac-Higgs theory: Particlelike solutions and their energy spectrum,” Phys. Rev. D 99, 076009 (2019).
2. Kojo and N. Su, “The quark mass gap in a magnetic field,” Phys. Lett. B 720, 192 (2013).
3. V. Dzhunushaliev, V. Folomeev and A. Serikbolova, “Monopole solutions in SU(2) Yang-Mills-plus-massive-nonlinear-spinor-field theory” Physics Letters B Volume 806, 135480 (2020).

In quantum gravity, it is expected that their will be some minimum length scale on possible states of the system. This is derived from modifying the standard quantum position and momentum operators to get a strictly positive lower bound on the uncertainty of position. It is generally thought that a modified commutator of the form $[{\hat x}, {\hat p}] = i \hbar (1 + \beta p^2)$ is sufficient to give rise to a minimum length scale. We test this assumption by presenting several different families of modified operators which all lead to the same modified commutator and demonstrating that each family has a different minimum length scale and even no minimal length. We do this by checking the uncertainty in position directly. This is due to the modified operators a subtly different uncertainty principle. The conclusion is that the modification of the operators is the main factor in determining whether there is a minimal length. This fact - that it is the specific form of the modified operators which determine the existence or not of a minimal length scale - can be used to keep or reject specific modifications of the position and momentum operators in theory of quantum gravity. This is joint work with Jaeyeong Lee and Douglas Singleton from the physics department.

It has been shown beyond reasonable doubt that the majority (about 95%) of the total energy budget of the universe is given by the dark constituents, namely Dark Matter and Dark Energy. What constitutes Dark Matter and Dark Energy remains to be satisfactorily understood however, despite a number of promising candidates. An associated conundrum is that of the coincidence, i.e. the question as to why the Dark Matter and Dark Energy densities are of the same order of magnitude at the present epoch, after evolving over the entire expansion history of the universe. In an attempt to address these, we consider a quantum potential resulting from a quantum corrected Raychaudhuri/Friedmann Equation in presence of a cosmic fluid, which is presumed to be a Bose-Einstein condensate (BEC) of ultralight bosons. For a suitable and physically motivated macroscopic ground state wavefunction of the BEC, we show that a unified picture of the cosmic dark sector can indeed emerge, which also resolves the issue of the coincidence. The effective density of the Dark energy component turns out to be a cosmological constant, by virtue of a residual homogeneous term in the quantum potential.Furthermore, comparison with observed data give an estimate of the mass of the constituent bosons in the BEC, which is well within the bounds predicted from other considerations.

Although the present universe is believed to be homogeneous and isotropic on large scales, there is some evidence of some anisotropy at early times, Hence, there is interest in the Bianchi models, which are homogeneous, but anisotropic. In this presentation, the Bianchi type–I space-time in the framework of the f(R,T) modified theory of gravity has been investigated for the specific choice of f(R,T) = R + 2f(T), where f(T) = - mT, m = constant. The solution of the modified gravity field equations has been generated by assuming that the deceleration parameter q is a simple linear function of the Hubble parameter H, i.e., q = b - d/H, (where b and d are constants, and d > 0 ) which yields the scale factor a = k[exp(dt) - 1]^1/(1+b) (where k is a constant). The model exhibits deceleration at early times, and is currently accelerating. It is also seen that the model approaches isotropy at late times. Expressions for the Hubble parameter in terms of red-shift, luminosity distance, and state-finder parameter are derived and their significance is described in detail. The physical properties of the cosmological model are also discussed. An interesting feature of the model is that it has a dynamic cosmological parameter, which is large during the early universe, decreases with time, and approaches a constant at late times. This may help in solving the cosmological constant problem.

The Planck Legacy recent release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB), which is higher than that estimated by the lambda cold dark matter model (ΛCDM). This endorses a closed and positively curved early Universe with a confidence level greater than 99%. In this study, quantised spacetime worldlines are utilised to model the evolution of the Universe in reference to the scale factor of the early Universe and its radius of curvature. The worldlines revealed both positive and negative solutions, implying that matter and antimatter of the early Universe plasma evolved in opposite directions away from each other as distinct sides of the Universe during a first decelerating phase. The worldlines then showed a second accelerated phase in reversed directions, where both sides could be free-falling towards each other under gravitational acceleration. Simulations of the spacetime continuum flux through its travel along predicted worldlines demonstrated the fast-orbital speed of stars resulting from external fields exerted on galaxies via the spatial curvature through the imaginary time dimension. Finally, the worldlines predicted a final time-reversal phase of rapid spatial contraction leading to a Big Crunch, signalling a cyclic Universe. These findings indicate that antimatter could exist as a distinct side, which influences the universe evolution; physically explaining the effects attributed to dark matter and dark energy.

We investigate the dynamics of galaxies with Refracted Gravity (RG), a novel classical theory of modified gravity inspired to electrodynamics in matter, which does not resort to dark matter. The presence of dark matter is mimicked by a gravitational permittivity, a monotonic increasing function of the local mass density which depends on three universal parameters.

RG properly describes the rotation curves and the vertical velocity dispersions of 30 disk galaxies from the DiskMass Survey (DMS) with mass-to-light ratios consistent with stellar population synthesis (SPS) models, disk scale heights in agreement with edge-on galaxies observations, and RG parameters from individual galaxies consistent with each other, suggesting their universality. RG produces a Radial Acceleration Relation of DMS galaxies with the correct asymptotic limits but with residuals correlating with some galaxy properties and with a too large intrinsic scatter, at odds with observations. Further investigation is required to assess if this issue indicates a failure of RG or depends on the galaxy sample.

RG also models the velocity dispersions of stars and of blue and red globular clusters of the elliptical E0 galaxies NGC 1407, NGC 4486, and NGC 5846 belonging to the SLUGGS survey with mass-to-light ratios in agreement with SPS predictions, anisotropy parameters consistent with the literature, and the three RG parameters in agreement with each other. Two out of three RG parameters are also consistent with those estimated from the DMS galaxies.

Given these encouraging results, RG is a theory that deserves further investigation.

We study the growth of linear matter density perturbations in a modified gravity approach of scalar field couplings with metric and torsion. In the equivalent scalar-tensor formulation, the matter fields in the Einstein frame interact as usual with an effective dark energy component, whose dynamics is presumably governed by a scalar field that sources a torsion mode. As a consequence, the matter density ceases to be self-conserved, thereby making an impact not only on the background cosmological evolution but also on the perturbative spectrum of the local inhomogeneities. In order to estimate the effect on the growth of the linear matter perturbations, with the least possible alteration of the standard parametric form of the growth factor, we resort to a suitable Taylor expansion of the corresponding exponent, known as the growth index, about the value of the cosmic scale factor at the present epoch. In particular, we obtain an appropriate fitting formula for the growth index in terms of the coupling function and the matter density parameter. While the overall parametric formulation of the growth factor is found to fit well with the latest redshift-space-distorsion (RSD) and the observational Hubble (OH) data at low redshifts, the fitting formula enables us to constrain the growth index to well within the concordant cosmological limits, thus ensuring the viability of the formalism.