Space, Matter and Interactions in a Quantum Early Universe. Part II: Superalgebras and Vertex Algebras

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra gu that extends e9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn gu into a Lie superalgebra sgu with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on sgu, which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular resonant scattering. Finally, we complete the model by merging the local sgu into a vertex-type algebra.

Symmetry Energy and the Pauli Exclusion Principle

In this article we present a classical potential that respects the Pauli exclusion principle and can be used to describe nucleon-nucleon interactions at intermediate energies. The potential depends on the relative momentum of the colliding nucleons and reduces interactions at low momentum transfer mimicking the Pauli exclusion principle. We use the potential with Metropolis Monte Carlo methods and study the formation of finite nuclei and infinite systems. We find good agreement in terms of the binding energies, radii, and internal nucleon distribution of finite nuclei, and the binding energy in nuclear matter and neutron star matter, as well as the formation of nuclear pastas, and the symmetry energy of neutron star matter.

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermality of Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters $$\sin \theta $$ sin θ and $$\Delta m$$ Δ m . As opposed to bosons, we find $$q>1$$ q > 1 , which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

How Quarks can be derived to Weak Interaction and Spin Classification with respect to the Pauli Exclusion

In this paper, we will strive to derive how quarks relate to spin classification and weak interactions with respect to the Pauli exclusion principle. Papers such as [2] and [3] inspired us to investigate quarks and their connections to weak interaction and spin classification. Being able to understand the inner workings of quarks would help scientists understand how physics work at the smallest level. By deriving it to contemporary physics concepts such as weak interaction, it would allow us to understand how very recent discoveries such as quarks work in the presence of interactions not designed for them. We will present research that attempt to construct how quarks work in weak interactions and prove how quarks play a crucial part in spin classification through using quark models that show why quarks are constrained by the Pauli exclusion principle and tables that show how they affect spin classification through their own properties and spin identifiers. Understanding these interactions will help contribute to every physicist always growing understanding of quarks and will help integrate modeling into the studying of quarks. Quarks are a crucial part of physics at the smallest level and this paper will contribute to knowledge already known and could be used to help other scientists learn more and publish new research about quarks.

Fundamental Theory of Torsion Gravity

In this work, we present the general differential geometry of a background in which the space–time has both torsion and curvature with internal symmetries being described by gauge fields, and that is equipped to couple spinorial matter fields having spin and energy as well as gauge currents: torsion will turn out to be equivalent to an axial-vector massive Proca field and, because the spinor can be decomposed in its two chiral projections, torsion can be thought as the mediator that keeps spinors in stable configurations; we will justify this claim by studying some limiting situations. We will then proceed with a second chapter, where the material presented in the first chapter will be applied to specific systems in order to solve problems that seems to affect theories without torsion: hence the problem of gravitational singularity formation and positivity of the energy are the most important, and they will also lead the way for a discussion about the Pauli exclusion principle and the concept of macroscopic approximation. In a third and final chapter, we are going to investigate, in the light of torsion dynamics, some of the open problems in the standard models of particles and cosmology which would not be easily solvable otherwise.

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.