scholarly journals RENORMALIZATION OF COUPLINGS IN EMBEDDED RANDOM SURFACES

1992 ◽  
Vol 07 (40) ◽  
pp. 3747-3757
Author(s):  
SUMIT R. DAS ◽  
S. KALYANA RAMA
Keyword(s):  
Phase Space ◽  
Extra Dimension ◽  
Extrinsic Curvature ◽  
String Tension ◽  
Length Scale ◽  
Random Surfaces ◽  
Curvature Term ◽  
Composite Field ◽  
Physical Scale ◽  
The Relationship

We study the dressing of operators and flows of corresponding couplings in models of embedded random surfaces. We show that these dressings can be obtained by applying the methods of David and Distler and Kawai. We consider two extreme limits. In the first limit the string tension is large and the dynamics is dominated by the Nambu-Goto term. We analyze this theory around a classical solution in the situation where the length scale of the solution is large compared to the length scale set by the string tension. Couplings get dressed by the Liouville mode (which is now a composite field) in a non-trivial fashion. However this does not imply that the excitations around a physical “long string” have a phase space corresponding to an extra dimension. In the second limit the string tension is small and the dynamics is governed by the extrinsic curvature term. We show, perturbatively, that in this theory the relationship between the induced metric and the worldsheet metric is “renormalized,” while the extrinsic curvature term receives a non-trivial dressing as well. This has the consequence that in a generic situation the dependence of couplings on the physical scale is different from that predicted by their beta functions.

scholarly journals SPECTRUM OF THE LOOP TRANSFER MATRIX ON FINITE LATTICES

2001 ◽  
Vol 16 (16) ◽  
pp. 1069-1077 ◽  
Author(s):  
GEORGIOS DASKALAKIS ◽  
GEORGE K. SAVVIDY
Keyword(s):  
Transfer Matrix ◽  
Phase Structure ◽  
Extrinsic Curvature ◽  
Critical Behaviour ◽  
Equivalent Representation ◽  
Random Surfaces ◽  
Finite Dimensional ◽  
Curvature Term ◽  
Finite Lattices ◽  
Euclidean Lattice

We consider a model of random surfaces with extrinsic curvature term embedded into 3-D Euclidean lattice Z3. On a 3-D Euclidean lattice it has an equivalent representation in terms of the transfer matrix K(Qi, Qf), which describes the propagation of the loops Q. We study the spectrum of the transfer matrix K(Qi, Qf) on finite-dimensional lattices. The renormalisation group technique is used to investigate the phase structure of the model and its critical behaviour.

scholarly journals LAGRANGIAN FORMULATION OF A MAGNETOSTATIC FIELD IN THE PRESENCE OF A MINIMAL LENGTH SCALE BASED ON THE KEMPF ALGEBRA

2013 ◽  
Vol 28 (30) ◽  
pp. 1350142 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
B. KHOSROPOUR
Keyword(s):  
Integral Form ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Lagrangian Formulation ◽  
Length Scale ◽  
Magnetostatic Field ◽  
Classical Level ◽  
Spatial Dimensions ◽  
Minimal Length Scale ◽  
The Relationship

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β′)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length [Formula: see text]. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β′ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee–Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot–Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19m. The relationship between magnetostatics with a minimal length and the Gaete–Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

scholarly journals Scaling laws and phase space analysis of a geomagnetic domino model

2021 ◽  
Vol 2090 (1) ◽  
pp. 012030
Author(s):  
K Peqini ◽  
D Prenga ◽  
R Osmanaj
Keyword(s):  
Phase Space ◽  
Scaling Laws ◽  
Outer Core ◽  
Main Field ◽  
Field Reversal ◽  
Core Dynamics ◽  
The Mean ◽  
Reversed Polarity ◽  
The Relationship ◽  
Mean Time

Abstract The geomagnetic field is among the most striking features of the Earth. By far the most important ingredient of it is generate in the fluid conductive outer core and it is known as the main field. It is characterized by a strong dipolar component as measured on the Earth’s surface. It is well established the fact that the dipolar component has reversed polarity many times, a phenomenon dubbed as dipolar field reversal (DFR). There have been proposed numerous models focused on describing the statistical features of the occurrence of such phenomena. One of them is the domino model, a simple toy model that despite its simplicity displays a very rich dynamic. This model incorporates several aspects of the outer core dynamics like the effect of rotation of Earth, the appearance of convective columns which create their own magnetic field, etc. In this paper we analyse the phase space of parameters of the model and identify several regimes. The two main regimes are the polarity changing one and the regime where the polarity remains the same. Also, we draw some scaling laws that characterize the relationship between the parameters and the mean time between reversals (mtr), the main output of the model.

The physical scale from string tension in LQCD

2019 ◽  
Author(s):  
Dafina Hyka-Xhako ◽  
Rudina Osmanaj ◽  
Joan Jani
Keyword(s):  
String Tension ◽  
Physical Scale

scholarly journals Confinement of Fermions in Tachyon Matter

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Adamu Issifu ◽  
Francisco A. Brito
Keyword(s):  
Tachyon Condensation ◽  
String Tension ◽  
Dielectric Medium ◽  
Higgs Mechanism ◽  
Quark Masses ◽  
Vector Dominance ◽  
Fermion Fields ◽  
Consistent Manner ◽  
Qcd String ◽  
The Relationship

In this paper, we develop a phenomenological model inspired by QCD that mimics the QCD theory. We use the gauge theory in color dielectric medium (Gϕ) coupled with fermion fields to produce scalar and vector confinements in the chromoelectric flux tube scenario. The Abelian theory will be used to approximate the non-Abelian QCD theory in a consistent manner. We will calculate vector and scalar glueballs and compare the result to the existing simulation and experimental results and projections. The QCD-like vacuum associated with the model will be calculated and its behavior studied relative to changing quark masses. We will also comment on the relationship between tachyon condensation, dual Higgs mechanism, QCD monopole condensation, and their association with confinement. The behavior of the QCD string tension obtained from the vector potential of the model will be studied to establish vector dominance in confinement theories.

scholarly journals Energy and time as conjugate dynamical variables

2000 ◽  
Vol 78 (11) ◽  
pp. 959-967 ◽  
Author(s):  
M Grigorescu
Keyword(s):  
Phase Space ◽  
Canonical Quantization ◽  
Constant Factor ◽  
Extended Phase Space ◽  
Moving Frames ◽  
Equivalence Group ◽  
Extended Phase ◽  
Classical Level ◽  
Time Variables ◽  
The Relationship

The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivariant. Although it has no effect at a classical level, the lack of equivariance makes the Galilei action inconsistent with the canonical quantization. A Hamiltonian equivariant action can be obtained by assuming that the inertial parameter in the extended phase-space is quasi-isotropic. This condition leads naturally to the Lorentz transformations between moving frames as a particular case of symplectic transformations. The limit speed appears as a constant factor relating the two additional canonical coordinates to the energy and time. Its value is identified with the speed of light by using the relationship between the electromagnetic potentials and the symplectic form of the extended phase-space. PACS Nos.: 45.20Jj, 11.30Cp, 03.50De

Weak self-avoidance and crumpling in random surfaces with extrinsic curvature

1991 ◽  
Vol 273 (4) ◽  
pp. 380-388 ◽  
Author(s):  
C.F. Baillie ◽  
D.A. Johnston
Keyword(s):  
Extrinsic Curvature ◽  
Random Surfaces
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