scholarly journals Dirac quantization of two-dimensional dilation gravity minimally coupled toNmassless scalar fields

1997 ◽  
Vol 55 (12) ◽  
pp. 7982-7984 ◽  
Author(s):  
Domingo Louis-Martinez
Keyword(s):  
Scalar Fields ◽  
Two Dimensional ◽  
Dirac Quantization ◽  
Dilation Gravity

Properties of Spatial-Rotation Transformations of Fractional Derivatives

2020 ◽  
pp. 198-223
Author(s):  
Ehab Malkawi
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivatives ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Two Dimensional ◽  
Spatial Rotation ◽  
Essential Step ◽  
Derivatives Of

The transformation properties of the fractional derivatives under spatial rotation in two-dimensional space and for both the Riemann-Liouville and Caputo definitions are investigated and derived in their general form. In particular, the transformation properties of the fractional derivatives acting on scalar fields are studied and discussed. The study of the transformation properties of fractional derivatives is an essential step for the formulation of fractional calculus in multi-dimensional space. The inclusion of fractional calculus in the Lagrangian and Hamiltonian dynamical formulation relies on such transformation. Specific examples on the transformation of the fractional derivatives of scalar fields are discussed.

scholarly journals Analytic reconstruction of a two-dimensional velocity field from an observed diffusive scalar

2019 ◽  
Vol 871 ◽  
pp. 755-774
Author(s):  
Arjun Sharma ◽  
Irina I. Rypina ◽  
Ruth Musgrave ◽  
George Haller
Keyword(s):  
Velocity Field ◽  
Ocean Circulation ◽  
Incompressible Flows ◽  
Circulation Model ◽  
Scalar Fields ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Velocity Measurements ◽  
Ocean Circulation Model ◽  
Spatial Domains

Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved if high-resolution tracer measurements, as well as velocity measurements along a curve transverse to the instantaneous scalar contours, are available. Such measurements enable solving a system of partial differential equations for the velocity components by the method of characteristics. If the value of the scalar diffusivity is known, then knowledge of just one velocity component along a transverse initial curve is sufficient. These conclusions extend to the shallow-water equations and to flows with spatially dependent diffusivity. We illustrate our results on velocity reconstruction from tracer fields for planar Navier–Stokes flows and for a barotropic ocean circulation model. We also discuss the use of the proposed velocity reconstruction in oceanographic applications to extend localized velocity measurements to larger spatial domains with the help of remotely sensed scalar fields.

ON A PHASE STRUCTURE OF A TWO-DIMENSIONAL (φ2)2 FIELD THEORY

1989 ◽  
Vol 04 (18) ◽  
pp. 4977-4990 ◽  
Author(s):  
G. V. EFIMOV
Keyword(s):  
Field Theory ◽  
Phase Transitions ◽  
Phase Structure ◽  
Weak Coupling ◽  
Scalar Fields ◽  
Perturbation Series ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Effective Coupling ◽  
Two Phases

Two models of scalar fields with the interaction Lagrangians gφ4 and [Formula: see text] are considered in ℝ2. There are phase transitions in these models for a certain g = gc. It is shown that the spontaneous symmetry breaking takes place for g > gc. The description of the two phases for g < gc and g > gc is given. The effective coupling constants in perturbation series are less than unity for both the phases so that these models describe the systems with weak coupling. In the second model the "Goldstone" particles have nonzero masses in the phase g > gc.

scholarly journals HAWKING RADIATION FOR SCALAR AND DIRAC FIELDS IN FIVE-DIMENSIONAL DILATONIC BLACK HOLE VIA ANOMALIES

2012 ◽  
Vol 21 (03) ◽  
pp. 1250030 ◽  
Author(s):  
RAMÓN BECAR ◽  
P. A. GONZÁLEZ
Keyword(s):  
Black Hole ◽  
Gauge Invariance ◽  
Scalar Fields ◽  
Two Dimensional ◽  
Massive Scalar ◽  
Dimensional Theory ◽  
Dirac Fields ◽  
Black Hole Background ◽  
Planck Distribution ◽  
Dilatonic Black Hole

We study massive scalar fields and Dirac fields propagating in a five-dimensional dilatonic black hole background. We expose that for both fields the physics can be described by a two-dimensional theory, near the horizon. Then, in this limit, by applying the covariant anomalies method we find the Hawking flux by restoring the gauge invariance and the general coordinate covariance, which coincides with the flux obtained from integrating the Planck distribution for fermions.

Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows

1990 ◽  
Vol 216 ◽  
pp. 1-34 ◽  
Author(s):  
Rahul R. Prasad ◽  
K. R. Sreenivasan
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Working Fluid ◽  
Small Scale ◽  
Main Body ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Two Dimensional Images

The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.

scholarly journals The spectral dimension in 2D CDT gravity coupled to scalar fields

2015 ◽  
Vol 30 (13) ◽  
pp. 1550077 ◽  
Author(s):  
J. Ambjørn ◽  
A. Görlich ◽  
J. Jurkiewicz ◽  
H. Zhang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Spectral Dimension ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Two Dimensional ◽  
Imaginary Time ◽  
Causal Dynamical Triangulations ◽  
Pure Gravity ◽  
Dynamical Triangulations

Causal Dynamical Triangulations (CDT) provide a non-perturbative formulation of Quantum Gravity assuming the existence of a global time foliation. In our earlier study we analyzed the effect of including d copies of a massless scalar field in the two-dimensional CDT model with imaginary time. For d > 1 we observed the formation of a "blob", somewhat similar to that observed in four-dimensional CDT without matter. In the two-dimensional case the "blob" has a Hausdorff dimension DH = 3. In this paper, we study the spectral dimension DS of the two-dimensional CDT-universe, both for d = 0 (pure gravity) and d = 4. We show that in both cases the spectral dimension is consistent with DS = 2.

TWO-DIMENSIONAL (HALF-) INTEGER SPIN CONFORMAL THEORIES WITH CENTRAL CHARGE c<1

1988 ◽  
Vol 03 (12) ◽  
pp. 2945-2958 ◽  
Author(s):  
V.B. PETKOVA
Keyword(s):  
Ising Model ◽  
Integral Representation ◽  
Central Charge ◽  
Scalar Fields ◽  
Operator Product ◽  
Two Dimensional ◽  
Model Order ◽  
Integer Spin ◽  
Half Integer ◽  
Spin Fields

A generalized integral representation involving two types of charges is explored to construct correlation functions on the plane for c=1–6/(m(m+1))<1 discrete unitary Virasoro series. The various local operator product algebras emerging contain integer, or half-integer, spin fields along with scalar fields. The examples also include a generalization for arbitrary m of the ℤ2-statistics of the Ising model order-disorder fields.

MACROSCOPIC BOUNDARIES AND THE WAVE FUNCTION OF THE UNIVERSE IN THE c=-2 MATRIX MODEL

1991 ◽  
Vol 06 (31) ◽  
pp. 2901-2908 ◽  
Author(s):  
JONATHAN D. EDWARDS ◽  
IGOR R. KLEBANOV
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Matrix Model ◽  
Ground State ◽  
Bessel Functions ◽  
Scalar Fields ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Genus Expansion ◽  
The Universe

Using a matrix model, we calculate sums over surfaces with macroscopic boundaries of fixed lengths in two-dimensional gravity coupled to a pair of anti-commuting scalar fields with c=-2. For n boundaries, the answer depends only on the sum of their lengths and is given explicitly in terms of Bessel functions to all orders of the genus expansion. For n=1, this defines the Hartle-Hawking ground state wave function of the universe, which is shown to satisfy the minisuperspace Wheeler–De Witt equation with a boundary condition imposed at small geometries.

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