Charge specific baryon mass relations with deformed SU_q(3) flavor symmetry

The quantum group $SU_q(3)=U_q(su(3))$ is taken as a baryon flavor symmetry. Accounting for electromagnetic contributions to baryons masses to zeroth order, new charge specific $q$-deformed octet and decuplet baryon mass formulas are obtained. These new mass relations have errors of only 0.02\% and 0.08\% respectively; a factor of 20 reduction compared to the standard Gell-Mann-Okubo mass formulas. A new relation between the octet and decuplet baryon masses that is accurate to 1.2\% is derived. An explicit formula for the Cabibbo angle, taken to be $\frac{\pi}{14}$, in terms of the deformation parameter $q$ and spin parity $J^P$ of the baryons is obtained.Comment: 14 page

Deformations of spacetime and internal symmetries

Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group $SU(3)$ to the quantum group $SU_q(3)\equiv U_q(su(3))$ (a Hopf algebra) and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly with experimental data.Comment: 5th International Conference on New Frontiers in Physics, Crete, Greece, July 6-14, 201

The Standard Model particle content with complete gauge symmetries from the minimal ideals of two Clifford algebras

Building upon previous works, it is shown that two minimal left ideals of the complex Clifford algebra $\mathbb{C}\ell(6)$ and two minimal right ideals of $\mathbb{C}\ell(4)$ transform as one generation of leptons and quarks under the gauge symmetry $SU(3)_C\times U(1)_{EM}$ and $SU(2)_L\times U(1)_Y$ respectively. The $SU(2)_L$ weak symmetries are naturally chiral. Combining the $\mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$ ideals, all the gauge symmetries of the Standard Model, together with its lepton and quark content for a single generation are represented, with the dimensions of the minimal ideals dictating the number of distinct physical states. The combined ideals can be written as minimal left ideals of $\mathbb{C}\ell(6)\otimes\mathbb{C}\ell(4)\cong \mathbb{C}\ell(10)$ in a way that preserves individually the $\mathbb{C}\ell(6)$ structure and $\mathbb{C}\ell(4)$ structure of physical states. This resulting model includes many of the attractive features of the Georgi and Glashow $SU(5)$ grand unified theory without introducing proton decay or other unobserved processes. Such processes are naturally excluded because they do not individually preserve the $\mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$ minimal ideals.Comment: 13 Page

Identifying and Predicting Financial Earthquakes Using Hawkes Processes

This dissertation attempts to identify and predict earthquakes in the financial market (financial crashes) using Hawkes processes. Models based on Hawkes processes were first used in the earthquake literature. The dissertation shows Hawkes processes also match investors' self-exciting herding behavior around crashes, which has similar characteristics to the self-exciting behavior of seismic activity around earthquakes. In Chapter 2 an Early Warning System based on Hawkes models is developed that indicates the arrival of a crash within a trading week. EWS based Hawkes model outperform EWS based on well-known and commonly used volatility models, proving that these models do not capture all information that can be used to predict crashes. Specification tests for Hawkes models with a specific focus on testing for cross-excitation, are designed in Chapter 3. Chapter 3 as well as Chapter 4, indicate that shocks in one financial market affect the occurrence (and magnitude) of shocks in other financial markets. Moreover, comparing predictions of models with and without cross-excitation, more accurate predictions are obtained including cross-excitation. The last Chapter (Chapter 5) develops methods to estimate non-affine Hawkes models using the information in option prices with the aid of Machine Learning techniques