arXiv subjects

E. G. Floratos

Publications and source records attributed to E. G. Floratos.

35 records · Page 2Linked to original sources

arXiv1999

The Matrix model and the non-commutative geometry of the supermembrane

This is a short note on the relation of the Matrix model with the non-commutative geometry of the 11-dimensional supermembrane. We put forward the idea that M-theory is described by the 't Hooft topological expansion of the Matrix model in the large N-limit where all topologies of membranes appear. This expansion can faithfully be represented by the Moyal Yang-Mills theory of membranes. We discuss this conjecture in the case of finite N, where the non-commutative geometry of the membrane is given be the finite quantum mechanics. The use of the finite dimensional representations of the Heisenberg group reveals the cellular structure of a toroidal supermembrane on which the Matrix model appears as a non-commutatutive Yang-Mills theory. The Moyal star product on the space of functions in the case of rational values of the Planck constant \hbar represents exactly this cellular structure. We also discuss the integrability of the instanton sector as well as the topological charge and the corresponding Bogomol'nyi bound.

hep-th↗

arXiv1999

Prime decomposition and correlation measure of finite quantum systems

Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $ρ$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of density matrices a complete tensor product factorization is achieved. The construction is based on the Chinese Remainder Theorem and the projective unitary representation of $Z_N$ by the discrete Heisenberg group $H_N$. The pd isomorphism is unitarily implemented and it is shown to be coassociative and to act on $H_N$ as comultiplication. Density matrices with complete pd are interpreted as grouplike elements of $H_N$. To quantify the distance of $ρ$ from its pd a trace-norm correlation index $\cal E$ is introduced and its invariance groups are determined.

quant-ph↗

arXiv1999

Low Scale Unification, Newton's Law and Extra Dimensions

Motivated by recent work on low energy unification, in this short note we derive corrections on Newton's inverse square law due to the existence of extra decompactified dimensions. In the four-dimensional macroscopic limit we find that the corrections are of Yukawa type. Inside the compactified space of n-extra dimensions the sub-leading term is proportional to the (n+1)- power of the distance over the compactification radius ratio. Some physical implications of these modifications are briefly discussed.

hep-ph↗

arXiv1998

Q-Balls and the Proton Stability in Supersymmetric Theories

Abelian non-topological solitons with Baryon and/or Lepton quantum numbers naturally appear in the spectrum of the minimal supersymmetric standard model. They arise as a consequence of the existence of flat directions in the potential lifted by non renormalizable operators and SUSY breaking. We examine the conditions that these operators should satisfy in order to ensure proton stability and present a realistic string model which fulfils these requirements. We further identify a generic U(1) breaking term in the scalar potential and discuss its effect of rendering Q-balls unstable.

hep-ph↗

arXiv1998

Fast Quantum Maps

We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.

math-ph↗

arXiv1998

An SU(2) Analog of the Azbel--Hofstadter Hamiltonian

Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a specific spin-S Euler top and can be considered as its ``classical'' analog. The eigenvalue problem for the proposed model, in the coherent state representation, is described by the S-gap Lamé equation and, thus, is completely solvable. We observe a striking similarity between the shapes of the spectra of the two models for various values of the spin S.

hep-th↗

arXiv1998

Eight-Dimensional Self-Dual Spaces

We discuss higher-dimensional gravitational instantons by studying appropriate self-duality equations for the spin connection. In seven and in eight dimensions, the corresponding spaces admit a covariantly constant spinor and have holonomies in G_2 and Spin(7), respectively. We find a non-compact solution to the self-duality equations in eight dimensions in which the self-dual space has an elliptically-fibered structure.

hep-th↗

arXiv1998

A Note on the Supersymmetries of the Self-Dual Supermembrane

In this letter we discuss the supersymmetry issue of the self dual supermembranes in (8+1) and (4+1)-dimensions. We find that all genuine solutions of the (8+1)-dimensional supermembrane, based on the exceptional group G_2, preserve one of the sixteen supersymmetries while all solutions in (4+1)-dimensions preserve eight of them.

hep-th↗

arXiv1997

On The Instanton Solutions Of The Self-Dual Membrane In Various Dimensions

We present some methods of determining explicit solutions for self-dual supermembranes in 4+1 and 8+1 dimensions with spherical or toroidal topology. For configurations of axial symmetry, the continuous SU(\infty) Toda equation turns out to play a central role, and a specific method of determining all the periodic solutions are suggested. A number of examples are studied in detail.

hep-th↗

arXiv1997

Octonionic Selfduality for SuperMembranes

In this work we study the recently introduced octonionic duality for membranes. Restricting the self - duality equations to seven space dimensions, we provide various forms for them which exhibit the symmetries of the octonionic and quaternionic structure. These forms may turn to be useful for the question of the integrability of this system. Introducing a consistent quadratic Poisson algebra of functions on the membrane we are able to factorize the time dependence of the self - duality equations. We further give the general linear embeddings of the three dimensional system into the seven dimensional one using the invariance of the self-duality equations under the exceptional group G_2.

hep-th↗

arXiv1997

Uncertainty relation and non-dispersive states in Finite Quantum Mechanics

In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an effective $\hbar$) vanishes. The classical regime, contrary to standard Quantum Mechanical Systems of particles and fields, but also of strings and branes appears in short distances of the order of the lattice spacing. {}For linear quantum maps of long periods, we observe that time evolution leads to fast decorrelation of the wave packets, phenomenon similar to the behavior of wave packets in t' Hooft and Susskind holographic picture. Moreoever, we construct explicitly a non - dispersive basis of states in accordance with t' Hooft's arguments about the deterministic behavior of FQM.

hep-th↗

arXiv1997

K-system generator of pseudorandom numbers on Galois field

We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on rational sublattice which coincides with the Galois field. The period of the trajectories increases as a function of lattice size and the dimension of the K-matrix. We emphasize the connection of this approach with the one which is based on primitive matrices over Galois fields.

physics.comp-ph↗

arXiv1996

Holomorphic Quantization on the Torus and Finite Quantum Mechanics

We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup $SL(2, Z)/Γ_l$, $Γ_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.

hep-th↗

arXiv1996

Period of K System Generator of Pseudorandom Numbers

We analyze the structure of the periodic trajectories of the matrix generator of pseudorandom numbers which has been proposed earlier. The structure of the periodic trajectories becomes more transparent when the rational sublattice coincides with the Galois field $GF[p]$. We are able to compute the period of the trajectories as a function of $p$ and the dimension of the matrix $d$.

hep-lat↗

arXiv1995

MSSM phenomenology in the large tanb regime

We discuss aspects of the low energy phenomenology of the MSSM, in the large $\tan β $ regime. We explore the regions of the parameter space where the $h_t$ and $h_b$ Yukawa couplings exhibit a fixed point structure, using previous analytic solutions for these couplings. Expressions for the parameters $A_{t}$ and $A_{b}$ and the renormalised soft mass terms are also derived, making it possible to estimate analytically the sparticle loop -- corrections to the bottom mass, which are important in this limit.

hep-ph↗

arXiv1995

Analytic Approach to the MSSM Mass Spectrum in the Large Tan$β$ Regime

In various unified extensions of the Minimal Supersymmetric Standard Model, the Yukawa couplings of the third generation are predicted to be of the same order. As a result, low energy measured mass ratios, require large ratios of the standard model Higgs vacuum expectation values, corresponding to a large value of the parameter $tanβ$. We present analytic solutions for the Yukawa couplings and the Higgs and third generation squark masses, in the case of large top and bottom Yukawa couplings. We examine regions of these Yukawas which give predictions for the top mass compatible with the present experimentally determined top mass and provide useful approximate formulae for the scalars. We discuss the implications on the Radiative Symmetry Breaking mechanism and derive constraints on the undetermined initial conditions of the scalars.

hep-ph↗

arXiv1994

Large Top and Bottom Yukawa Couplings in Minimal Supersymmetry

We present analytic expressions for the top and bottom Yukawa couplings in the context of the minimal supersymmetric standard model when both couplings $h_{t,0},h_{b,0}$ are large at the unification scale. For sufficiently large $h_{t,0},h_{b,0}$, i.e. within $\sim (20-25)\% $ close to their fixed point values, using as input the central value of the bottom mass $m_b(m_b)=4.25GeV$, we find that the top mass lies in the range $m_t \approx (174-178)GeV$, while $tanβ\approx (55-58)$. Implications on the evolution of the scalar masses and the radiative symmetry breaking scenario are discussed. %

hep-ph↗