scholarly journals Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1298 ◽  
Author(s):  
Torsten Asselmeyer-Maluga
Keyword(s):  
Number Theory ◽  
Particle Physics ◽  
Elementary Particles ◽  
Branched Covers ◽  
Particle Properties ◽  
Torus Bundles ◽  
Branched Cover ◽  
Knot Complements ◽  
The Right ◽  
Trace Fields

In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C ( K ) = S 3 \ ( K × D 2 ) of a knot K carrying a hyperbolic geometry) and bosons as torus bundles. In particular, hyperbolic 3-manifolds have a close connection to number theory (Bloch group, algebraic K-theory, quaternionic trace fields), which will be used in the description of fermions. Here, we choose the description of 3-manifolds by branched covers. Every 3-manifold can be described by a 3-fold branched cover of S 3 branched along a knot. In case of knot complements, one will obtain a 3-fold branched cover of the 3-disk D 3 branched along a 3-braid or 3-braids describing fermions. The whole approach will uncover new symmetries as induced by quantum and discrete groups. Using the Drinfeld–Turaev quantization, we will also construct a quantization so that quantum states correspond to knots. Particle properties like the electric charge must be expressed by topology, and we will obtain the right spectrum of possible values. Finally, we will get a connection to recent models of Furey, Stoica and Gresnigt using octonionic and quaternionic algebras with relations to 3-braids (Bilson–Thompson model).

scholarly journals Relaxing cosmological neutrino mass bounds with unstable neutrinos

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Miguel Escudero ◽  
Jacobo Lopez-Pavon ◽  
Nuria Rius ◽  
Stefan Sandner
Keyword(s):  
Neutrino Mass ◽  
Particle Physics ◽  
Goldstone Boson ◽  
Mass Scale ◽  
Simple Extension ◽  
Type I ◽  
Mass Generation ◽  
Age Of The Universe ◽  
Neutrino Mass Models ◽  
The Right

Abstract At present, cosmological observations set the most stringent bound on the neutrino mass scale. Within the standard cosmological model (ΛCDM), the Planck collaboration reports ∑mv< 0.12 eV at 95 % CL. This bound, taken at face value, excludes many neutrino mass models. However, unstable neutrinos, with lifetimes shorter than the age of the universe τν ≲ tU, represent a particle physics avenue to relax this constraint. Motivated by this fact, we present a taxonomy of neutrino decay modes, categorizing them in terms of particle content and final decay products. Taking into account the relevant phenomenological bounds, our analysis shows that 2-body decaying neutrinos into BSM particles are a promising option to relax cosmological neutrino mass bounds. We then build a simple extension of the type I seesaw scenario by adding one sterile state ν4 and a Goldstone boson ϕ, in which νi→ ν4ϕ decays can loosen the neutrino mass bounds up to ∑mv ∼ 1 eV, without spoiling the light neutrino mass generation mechanism. Remarkably, this is possible for a large range of the right-handed neutrino masses, from the electroweak up to the GUT scale. We successfully implement this idea in the context of minimal neutrino mass models based on a U(1)μ−τ flavor symmetry, which are otherwise in tension with the current bound on ∑mv.

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

scholarly journals PROBING GRAVITATIONAL INTERACTIONS OF ELEMENTARY PARTICLES

2004 ◽  
Vol 13 (10) ◽  
pp. 2355-2359 ◽  
Author(s):  
JONATHAN L. FENG ◽  
ARVIND RAJARAMAN ◽  
FUMIHIRO TAKAYAMA
Keyword(s):  
Dark Matter ◽  
Early Universe ◽  
Particle Physics ◽  
Gravitational Constant ◽  
Planck Scale ◽  
Elementary Particles ◽  
Supersymmetric Particle ◽  
Small Scales ◽  
Physics Experiments ◽  
Shed Light

The gravitational interactions of elementary particles are suppressed by the Planck scale M*~1018 GeV and are typically expected to be far too weak to be probed by experiments. We show that, contrary to conventional wisdom, such interactions may be studied by particle physics experiments in the next few years. As an example, we consider conventional supergravity with a stable gravitino as the lightest supersymmetric particle. The next-lightest supersymmetric particle (NLSP) decays to the gravitino through gravitational interactions after about a year. This lifetime can be measured by stopping NLSPs at colliders and observing their decays. Such studies will yield a measurement of Newton's gravitational constant on unprecedentedly small scales, shed light on dark matter, and provide a window on the early universe.

Removing the conspiracy of BSM physics and BSM cosmology

2019 ◽  
Vol 28 (13) ◽  
pp. 1941012 ◽  
Author(s):  
Maxim Yu. Khlopov
Keyword(s):  
Standard Model ◽  
Particle Physics ◽  
Elementary Particles ◽  
Physical Basis ◽  
Particle Model ◽  
Beyond The Standard Model ◽  
Cosmological Scenario ◽  
The Standard Model ◽  
Modern Cosmology ◽  
Bsm Physics

The standard model (SM) of elementary particles finds no contradictions in the experimental data, but appeals to extensions for solutions of its internal problems and physical basis of the modern cosmology. The latter is based on inflationary models with baryosynthesis and dark matter/energy that involves Physics beyond the standard model (BSM) of elementary particles. However, studies of the BSM physical basis of the modern cosmology inevitably reveals additional particle model-dependent cosmological consequences that go beyond the modern standard cosmological model. The mutual relationship of the BSM particle physics basis of the modern cosmology and the nontrivial features of the corresponding cosmological scenario are the subject of this paper.

ANALYTIC CONTINUATION OF OPERATORS APPLICATIONS: FROM NUMBER THEORY AND GROUP THEORY TO QUANTUM FIELD AND STRING THEORIES

1999 ◽  
Vol 11 (04) ◽  
pp. 463-501 ◽  
Author(s):  
S. C. WOON
Keyword(s):  
Number Theory ◽  
Analytic Continuation ◽  
Particle Physics ◽  
Fractional Derivatives ◽  
Bernoulli Polynomials ◽  
Local Effect ◽  
Quantum Field ◽  
Matrix Representations ◽  
Complex Power ◽  
Non Local

We are used to thinking of an operator acting once, twice, and so on. However, an operator can be analytically continued to the operator raised to a complex power. Applications include (s,r) diagrams and an extension of Fractional Calculus where commutativity of fractional derivatives is preserved, generating integrals and non-standard derivations of theorems in Number Theory, non-integer power series and breaking of Leibniz and Chain rules, pseudo-groups and symmetry deforming models in particle physics and cosmology, non-local effect in analytically continued matrix representations and its connection with noncommutative geometry, particle-physics-like scatterings of zeros of analytically continued Bernoulli polynomials, and analytic continuation of operators in QM, QFT and Strings.

scholarly journals CHARACTER VARIETIES OF ONCE-PUNCTURED TORUS BUNDLES WITH TUNNEL NUMBER ONE

2013 ◽  
Vol 24 (06) ◽  
pp. 1350048 ◽  
Author(s):  
KENNETH L. BAKER ◽  
KATHLEEN L. PETERSEN
Keyword(s):  
Boundary Component ◽  
Lens Space ◽  
Algebraic Sets ◽  
Character Varieties ◽  
Torus Bundles ◽  
Whitehead Link ◽  
Birational Equivalence ◽  
Punctured Torus ◽  
Tunnel Number ◽  
Trace Fields

We determine the PSL2(ℂ) and SL2(ℂ) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine "natural" models for these algebraic sets, identify them up to birational equivalence with smooth models, and compute the genera of the canonical components. This enables us to compare dilatations of the monodromies of these bundles with these genera. We also determine the minimal polynomials for the trace fields of these manifolds. Additionally, we study the action of the symmetries of these manifolds upon their character varieties, identify the characters of their lens space fillings, and compute the twisted Alexander polynomials for their representations to SL2(ℂ).

ALONGSIDE THE STANDARD MODEL: UNIFICATION VIA GEOMETRY

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 916-918
Author(s):  
J. S. Avrin
Keyword(s):  
Standard Model ◽  
Particle Physics ◽  
Geometrical Model ◽  
Elementary Particles ◽  
Conceptual Basis ◽  
Common Elements ◽  
The Standard Model

A geometrical model (GM) featuring a visualizable reduction of the elementary particles and interactions down to common elements has been developed. As a consequence, a taxonomy of particles and various interactions emerge, all in consonance with the Standard Model (SM) of particle physics. However, the GM goes well beyond the SM, incorporating a number of fundamental phenomena and issues for which the latter has no explanation. Since the GMs largely diagramatic development cannot be displayed in this brief paper, only a summary of its conceptual basis and consequences is presented herein.

ALEXANDER POLYNOMIALS AND ORDERS OF HOMOLOGY GROUPS OF BRANCHED COVERS OF KNOTS

2009 ◽  
Vol 18 (07) ◽  
pp. 973-984 ◽  
Author(s):  
SE-GOO KIM
Keyword(s):  
Prime Power ◽  
Alexander Polynomial ◽  
Branched Covers ◽  
Splitting Property ◽  
Homology Groups ◽  
Alexander Polynomials ◽  
Knot Concordance ◽  
Branched Cover ◽  
Linearly Independent

Fox showed that the order of homology of a cyclic branched cover of a knot is determined by its Alexander polynomial. We find examples of knots with relatively prime Alexander polynomials such that the first homology groups of their q-fold cyclic branched covers are of the same order for every prime power q. Furthermore, we show that these knots are linearly independent in the knot concordance group using the polynomial splitting property of the Casson–Gordon–Gilmer invariants.

scholarly journals Two-fold branched covers

2014 ◽  
Vol 23 (03) ◽  
pp. 1430001 ◽  
Author(s):  
David Auckly
Keyword(s):  
Finite Number ◽  
Three Dimensional ◽  
Dehn Surgery ◽  
Dimensional Sphere ◽  
Branched Covers ◽  
Additional Symmetries ◽  
Branched Cover

Many three-dimensional manifolds are two-fold branched covers of the three-dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and includes many examples. It shows that there are three-dimensional homology spheres that do not two-fold branched cover any manifold, ones that only two-fold branched cover the three-dimensional sphere, ones that just two-fold branched cover a non-trivial manifold, and ones that two-fold branched cover both the sphere and non-trivial manifolds. When a manifold is surgery on a knot, the possible quotients via involutions generically correspond to quotients of the knot. There can, however, be a finite number of surgeries for which there are exceptional additional symmetries. The included proof of this result follows the proof of Thurston's Dehn surgery theorem. The paper also includes examples of such exceptional symmetries. Since the quotients follow the behavior of knots, a census of the behavior for knots with less than 11 crossings is included.

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