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

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2289
Author(s):  
Piero Truini ◽  
Alessio Marrani ◽  
Michael Rios ◽  
Klee Irwin
Keyword(s):  
Quantum Gravity ◽  
Lie Algebra ◽  
Early Universe ◽  
Resonant Scattering ◽  
Pauli Exclusion Principle ◽  
Lie Superalgebra ◽  
Cartan Matrix ◽  
Exclusion Principle ◽  
Natural Action ◽  
Infinite Dimensional

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.

scholarly journals A Deformed Quon Algebra

2019 ◽  
Vol 27 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Hery Randriamaro
Keyword(s):  
Vector Space ◽  
Vacuum State ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Infinite Dimensional ◽  
Bose Statistics ◽  
Particle Statistics ◽  
Creation Operators

AbstractThe quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators ai,k, (i, k) ∈ ℕ* × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations {a_j}_{,l}a_{i,k}^\dagger = qa_{i,k}^\dagger{a_{j,l}} + {q^{{\beta _{k,l}}}}{\delta _{i,j}} We prove the realizability of our model by showing that, for suitable values of q, the vector space generated by the particle states obtained by applying combinations of ai,k’s and a_{i,k}^\dagger ‘s to a vacuum state |0〉 is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.

scholarly journals THE PAULI EXCLUSION PRINCIPLE AND SU(2) VERSUS SO(3) IN LOOP QUANTUM GRAVITY

2003 ◽  
Vol 12 (09) ◽  
pp. 1729-1736 ◽  
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Gauge Group ◽  
Loop Quantum Gravity ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Exclusion Principle ◽  
Spin Networks

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.

scholarly journals Space, Matter and Interactions in a Quantum Early Universe Part I: Kac–Moody and Borcherds Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2342
Author(s):  
Piero Truini ◽  
Alessio Marrani ◽  
Michael Rios ◽  
Klee Irwin
Keyword(s):  
Quantum Gravity ◽  
Lie Algebra ◽  
Early Universe ◽  
Quantum Model ◽  
Initial Condition ◽  
Particle Interactions ◽  
Early Stages ◽  
The Universe ◽  
Expansion Of Space ◽  
Matter And Interactions

We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac–Moody Lie algebra e9. We investigate Kac–Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.

Hardness and HOMO-LUMO Gap Probed by the Helium Atom Pushing the Molecular Surface of the First-Row Hydride Molecules

2003 ◽  
Vol 68 (12) ◽  
pp. 2344-2354 ◽  
Author(s):  
Edyta Małolepsza ◽  
Lucjan Piela
Keyword(s):  
Helium Atom ◽  
Pauli Exclusion Principle ◽  
Structure Change ◽  
Molecular Surface ◽  
Exclusion Principle ◽  
Probe Position ◽  
Repulsion Energy ◽  
Ionic Dissociation ◽  
Probe Site ◽  
Homo Lumo

A molecular surface defined as an isosurface of the valence repulsion energy may be hard or soft with respect to probe penetration. As a probe, the helium atom has been chosen. In addition, the Pauli exclusion principle makes the electronic structure change when the probe pushes the molecule (at a fixed positions of its nuclei). This results in a HOMO-LUMO gap dependence on the probe site on the isosurface. A smaller gap at a given probe position reflects a larger reactivity of the site with respect to the ionic dissociation.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

scholarly journals Polynomial ring representations of endomorphisms of exterior powers

2021 ◽  
Author(s):  
Ommolbanin Behzad ◽  
André Contiero ◽  
Letterio Gatto ◽  
Renato Vidal Martins
Keyword(s):  
Lie Algebra ◽  
Polynomial Ring ◽  
Vertex Operators ◽  
Exterior Power ◽  
Infinite Dimensional ◽  
Symmetric Structure ◽  
Rational Polynomials ◽  
Exterior Powers ◽  
Vertex Representation ◽  
Countably Infinite

AbstractAn explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.

scholarly journals Testing the Pauli Exclusion Principle for Electrons at LNGS

2015 ◽  
Vol 61 ◽  
pp. 552-559 ◽  
Author(s):  
H. Shi ◽  
S. Bartalucci ◽  
S. Bertolucci ◽  
C. Berucci ◽  
A.M. Bragadireanu ◽  
...  
Keyword(s):  
Pauli Exclusion Principle ◽  
Exclusion Principle
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