arXiv subjects

Michael McGuigan

Publications and source records attributed to Michael McGuigan.

46 records · Page 3Linked to original sources

arXiv2006

Cosmological Constant Seesaw in Quantum Cosmology

Recently a phenomenological relationship for the observed cosmological constant has been discussed by Motl and Carroll in the context of treating the cosmological constant as a $2\times 2$ matrix but no specific realization of the idea was provided. We realize a cosmological constant seesaw mechanism in the context of quantum cosmology. The main observation used is that a positive cosmological constant plays the role of a $Mass^2$ term in the Wheeler DeWitt (WDW) equation. Modifying the WDW equation to include a coupling between two universes, one of which has planck scale vacuum energy and another which has vacuum energy at the supersymmetry breaking scale before mixing, we obtain the relation $λ= (10TeV)^8/M_{Pl}^4$ in a similar manner to the usual seesaw mechanism. We discuss how the picture fits in with our current understanding of string/M-theory cosmologies. In particular we discuss how these results might be extended in the context of exact wave functions of the universe derived from certain string models.

hep-th↗

arXiv2005

Riemann Hypothesis and Short Distance Fermionic Green's Functions

We show that the Green's function of a two dimensional fermion with a modified dispersion relation and short distance parameter $a$ is given by the Lerch zeta function. The Green's function is defined on a cylinder of radius R and we show that the condition $R = a$ yields the Riemann zeta function as a quantum transition amplitude for the fermion. We formulate the Riemann hypothesis physically as a nonzero condition on the transition amplitude between two special states associated with the point of origin and a point half way around the cylinder each of which are fixed points of a $Z_2$ transformation. By studying partial sums we show that that the transition amplitude formulation is analogous to neutrino mixing in a low dimensional context. We also derive the thermal partition function of the fermionic theory and the thermal divergence at temperature $1/a.$ In an alternative harmonic oscillator formalism we discuss the relation to the fermionic description of two dimensional string theory and matrix models. Finally we derive various representations of the Green's function using energy momentum integrals, point particle path integrals, and string propagators.

math-ph↗

arXiv2004

Noncritical M-theory: Three Dimensions

At the macrosopic level we study candidate 3D effective field theories associated to M theory in three dimensions. These represent analogs of 11D supergravity for eleven dimensional M-theory. At the microscopic level we study various world volume (WV) theories that can be used to relate world sheet (WS) theories of two dimensional strings. These are better defined for 3D targets than their 11D counterparts in part because there are no transverse dimensions. In particular M-theory on the target manifold AdS3 and RxSL(2,R)/SO(2) are studied using a supermembrane and WV 3d gravity approach.

hep-th↗

arXiv2004

Interactive visualization of higher dimensional data in a multiview environment

We develop multiple view visualization of higher dimensional data. Our work was chiefly motivated by the need to extract insight from four dimensional Quantum Chromodynamic (QCD) data. We develop visualization where multiple views, generally views of 3D projections or slices of a higher dimensional data, are tightly coupled not only by their specific order but also by a view synchronizing interaction style, and an internally defined interaction language. The tight coupling of the different views allows a fast and well-coordinated exploration of the data. In particular, the visualization allowed us to easily make consistency checks of the 4D QCD data and to infer the correctness of particle properties calculations. The software developed was also successfully applied in material studies, in particular studies of meteorite properties. Our implementation uses the VTK API. To handle a large number of views (slices/projections) and to still maintain good resolution, we use IBM T221 display (3840 X 2400 pixels).

cs.GR↗

arXiv2004

Three Dimensional Gravity and M-Theory

It is well known that string theory can be formulated as two dimensional gravity coupled to matter. In the 2d gravity formulation the central charge of the matter together with a hidden dimension from the conformal factor or Liouville mode determines the Target space dimension. Also the vacuum amplitude of the 2d gravity formulation implies important constraints on the Target space theory associated with modular invariance. In this paper we study a three dimensional gravity approach to M-theory. We find that there are three hidden Liouville type fields coming from the 3d gravity sector and that these together with the number of zero modes of the matter fields determine an eleven dimensional Target space of M theory. We investigate the perturbative vacuum amplitude for the 3d gravity approach to M theory and constraints imposed from SL(3,Z) modular invariance using a method of Dolan and Nappi together with a sum over spin structures which generalizes the SL(2,Z) invariance found in string theory. To introduce gauge fields in M-theory we study the vacuum amplitude on a three annulus and introduce interactions with two dimensional matter on a boundary in analogy with the introduction of gauge fields for open string theory. We study a three dimensional version of M-theory from the 3d gravity perspective and show how it relates to two dimensional type 0A string theory described by a 2d superLiouville theory with c=1 matter and, on manifolds with boundary, to a E8xSO(8) 2d heterotic string. We discuss a nonperturbative 3d gravity approach to M-theory and the expansion about e=0 in the Chern-Simons gauge formulation of the theory. Finally we study the interaction of fermionic matter with 3d gravity to investigate the origins of conformal dimension and Liouville effective action from a 3d gravity approach.

hep-th↗

arXiv2003

Application of interactive parallel visualization for commodity-based clusters using visualization APIs

We present an efficient and inexpensive to develop application for interactive high-performance parallel visualization. We extend popular APIs such as Open Inventor and VTK to support commodity-based cluster visualization. Our implementation follows a standard master/slave concept: the general idea is to have a ``Master'' node, which will intercept a sequential graphical user interface (GUI) and broadcast it to the ``Slave'' nodes. The interactions between the nodes are implemented using MPI. The parallel remote rendering uses Chromium. This paper is mainly the report of our implementation experiences. We present in detail the proposed model and key aspects of its implementation. Also, we present performance measurements, we benchmark and quantitatively demonstrate the dependence of the visualization speed on the data size and the network bandwidth, and we identify the singularities and draw conclusions on Chromium's sort-first rendering architecture. The most original part of this work is the combined use of Open Inventor and Chromium.

cs.GR↗

arXiv2003

Quantum Cellular Automata from Lattice Field Theories

We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral and operator formalisms of lattice field theories. We show that the quantization of supersymmetric cellular automata is related to recently discussed string bit models of Thorn and Bergman and represents a link of cellular automata theory to fundamental physics. We discuss spin and quantum dot cellular automata for their importance in experimental realizations and their use in quantum computation. Previous studies of quantum cellular automata utilize the wave function values as cell contents and the discretized linear Dirac equation as an update equation. We show that our approach to the quantization of fermionic cellular automata includes this utilization as a field equation, and in addition allows for nonlinearity through lattice field interactions.

quant-ph↗

arXiv1994

Finite Black Hole Entropy and String Theory

An accelerating observer sees a thermal bath of radiation at the Hawking temperature which is proportional to the acceleration. Also, in string theory there is a Hagedorn temperature beyond which one cannot go without an infinite amount of energy. Several authors have shown that in the context of Hawking radiation a limiting temperature for string theory leads to a limiting acceleration, which for a black hole implies a minimum distance from the horizon for an observer to remain stationary. We argue that this effectively introduces a cutoff in Rindler space or the Schwarzschild geometry inside of which accelerations would exceed this maximum value. Furthermore, this natural cutoff in turn allows one to define a finite entropy for Rindler space or a black hole as all divergences were occurring on the horizon. In all cases if a particular relationship exists between Newton's constant and the string tension then the entropy of the string modes agrees with the Bekenstein-Hawking formula.

hep-th↗

arXiv1992

Third Quantization and Black Holes

Recent results on the quantum mechanics of black holes indicate that the spacetime singularity can be avoided if the space of fields is extended in its domain as well as the vanishing of beta functions required as an equation in target space. Such an approach seems to inevitably lead to the quantization in this space that is the so-called third quantization. We discuss some of the implications of third quantization for the physics of blackholes in two dimensions. By discretizing the transverse dimensions describing the horizon it may also be possible to describe regulated four dimensional gravity in this manner and perhaps shed some light on the meaning of black hole entropy.

hep-th↗

arXiv1992

Quark-Antiquark Regge Trajectories in Large N_c QCD

We apply methods developed by Lovelace, Lipatov and Kirschner to evaluate the leading Regge trajectories α(t) with the quantum numbers of nonexotic quark-antiquark mesons at N_c = infinity and in the limit of t going to minus infinity. In this region renormalization group improved perturbation theory should be valid. We discuss the compatibility of nonlinear trajectories with narrow resonance approximations.

hep-ph↗