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The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and…
In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the…
Based on the hierarchy exhibited by quarks masses at low energies, we assume that Yukawa couplings of up and down quarks are related by $Y_u\propto Y_d^2$ at grand unification scales. This ansatz gives rise to a symmetrical CKM matrix at…
The smallness and hierarchy in fermion parameters could be the result of selection rules due to an Abelian horizontal symmetry broken by a small parameter. When applied to the lepton sector, then for a large class of models, a number of…
We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, eg. with the commutator ($C$) of the lepton mass matrices. Introducing a strictly covariant…
Employing induced representations of the Lorentz group (Wigner's little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the S…
Within the broad context of quark-lepton unification, we investigate the implications of broken continuous family symmetries which result from requiring that in the limit of exact symmetry, the Dirac mass matrices yield hierarchical masses…
We describe a way to continue the fermionic renormalization group flow into phases with broken global symmetry. The method does not require a Hubbard-Stratonovich decoupling of the interaction. Instead an infinitesimally small…
By assuming there exist three massive non-degenerate Majorana neutrinos, it is possible to describe neutrino mixing with a residual, unbroken discrete Klein subgroup of a larger spontaneously broken flavor symmetry group. Motivated by…
The excess in electron recoil events reported recently by the XENON1T experiment may be interpreted as evidence for a sizable transition magnetic moment $\mu_{\nu_e\nu_\mu}$ of Majorana neutrinos. We show the consistency of this scenario…
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…
If neutrino masses have a radiative origin, their smallness can be naturally understood even when lepton number violation occurs near the weak scale. We analyze a specific model of this type wherein the neutrino masses arise as two--loop…
In this talk we present a powerful tool applied to the study of Leptonic Physics. This tool is based on the construction of Weak Basis invariant relations associated to different properties of leptonic models. The rationale behind these…
We work in theories with both light and heavy particles. A method to obtain an effective low energy action with respect to the light particle is presented. Thanks to Wilsonian renormalization, we obtain effective actions with finite number…
Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form…
A factorization of the inverse of a Hermetian positive definite matrix based on a diagonal by diagonal recurrence formulae permits the inversion of Block Toeplitz matrices, using only matrix-vector products, and with a complexity of…
We investigate the viability of thermal leptogenesis in type-I seesaw models with leptonic flavour symmetries that lead to tribimaximal neutrino mixing. We consider an effective theory with an A4 x Z3 x Z4 symmetry, which is spontaneously…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
We compute, on the $(\lambda \Phi^4)_{1+1}$ model on the lattice, the soliton mass by means of two very different numerical methods. First, we make use of a ``creation operator'' formalism, measuring the decay of a certain correlation…
We show that not only the hierarchical quark CKM mixing matrix but also the "bimaximal" lepton flavor mixing matrix can be derived from the same mass matrix ansatz based on the broken permutation symmetry, by assuming the hierarchy of…