The effective Lagrangian and the scale anomaly in the nonlinear σ model

1992 ◽  
Vol 70 (6) ◽  
pp. 455-457 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Dimensional Space ◽  
Two Dimensions ◽  
Feynman Diagrams ◽  
Two Dimensional ◽  
Standard Result ◽  
Weyl Geometry ◽  
Effective Lagrangian ◽  
Need To Evaluate ◽  
The One ◽  
Generally Covariant

We compute the one-loop effective Lagrangian for the generally covariant nonlinear σ model in two dimensions, using a technique of Bukbinder et al. This circumvents the need to evaluate Feynman diagrams and eliminates having to introduce a mass to serve as an infrared regulator. The two-dimensional space is assumed to have Weyl geometry. In the limit that the Weyl geometry becomes Riemannian, the standard result for the anomaly in the trace of the stress tensor is recovered.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

A Comparison of Diffusion Flame Stability in One and Two Spatial Dimensions Near Cold, Inert Surfaces

2001 ◽  
Author(s):  
Robert Vance ◽  
Indrek S. Wichman
Keyword(s):  
Two Dimensions ◽  
Low Flow ◽  
Dimensional System ◽  
Flame Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Cellular Flames ◽  
The One ◽  
Inert Surfaces

Abstract A linear stability analysis is performed on two simplified models representing a one-dimensional flame between oxidizer and fuel reservoirs and a two-dimensional “edge-flame” between the same reservoirs but above a cold, inert wall. Comparison of the eigenvalue spectra for both models is performed to discern the validity of extending the results from the one-dimensional problem to the two-dimensional problem. Of primary interest is the influence on flame stability of thermal-diffusive imbalances, i.e. non-unity Lewis numbers. Flame oscillations are observed when Le > 1, and cellular flames are witnessed when Le < 1. It is found that when Le > 1 the characteristics of flame behavior are consistent between the two models. Furthermore, when Le < 1, the models are found to be in good agreement with respect to the magnitude of the critical wave numbers. Results from the coarse mesh analysis of the two-dimensional system are presented and compared to the one-dimensional eigenvalue spectra. Additionally, an examination of low reactant convection is undertaken. It is concluded that for low flow rates the behavior in one and two dimensions are similar qualitatively and quantitatively.

A Hill-determinant approach to symmetric double-well potentials in two dimensions

1995 ◽  
Vol 73 (9-10) ◽  
pp. 632-637 ◽  
Author(s):  
M. R. M. Witwit ◽  
J. P. Killingbeck
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Degenerate Eigenvalues ◽  
Double Well Potential ◽  
Range Of Values

Energy levels of the Schrödinger equation for a double-well potential V(x,y;Z2,λ) = −Z2[x2 + y2] + λ[axxx4 + 2axyx2y2 + ayyy4] in two-dimensional space are calculated, using a Hill-determinant approach for several eigenstates and a range of values of λ and Z2. Special emphasis is placed on the larger values of Z2, for which the eigenvalues for different states have almost degenerate eigenvalues.

Nonmonocentric Urban Configurations in a Two-Dimensional Space

1989 ◽  
Vol 21 (3) ◽  
pp. 363-374 ◽  
Author(s):  
H Ogawa ◽  
M Fujita
Keyword(s):  
Land Use ◽  
Dimensional Space ◽  
Urban Land ◽  
Urban Land Use ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Circular Symmetry ◽  
One Dimensional ◽  
Urban Configurations ◽  
The One

A one-dimensional model of nonmonocentric urban land use is extended into a two-dimensional space. Under the assumption of circular symmetry, it is shown that the equilibrium urban configurations in the two-dimensional space are essentially the same as those in the one-dimensional space except for the conditions on the parameters.

scholarly journals Classical instanton solutions in quantum field theory

2020 ◽  
pp. 78-85
Author(s):  
Roman G. Shulyakovsky ◽  
Alexander S. Gribowsky ◽  
Alexander S. Garkun ◽  
Maxim N. Nevmerzhitsky ◽  
Alexei O. Shaplov ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
The One

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

scholarly journals The Statistical Properties of theq-Deformed Dirac Oscillator in One and Two Dimensions

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Dynamics ◽  
Relativistic Quantum ◽  
Small Deformation ◽  
Two Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
One Dimensional ◽  
Pure Phase ◽  
The One

We study the behavior of the eigenvalues of the one and two dimensions ofq-deformed Dirac oscillator. The eigensolutions have been obtained by using a method based on theq-deformed creation and annihilation operators in both dimensions. For a two-dimensional case, we have used the complex formalism which reduced the problem to a problem of one-dimensional case. The influence of theq-numbers on the eigenvalues has been well analyzed. Also, the connection between theq-oscillator and a quantum optics is well established. Finally, for very small deformationη, we (i) showed the existence of well-knownq-deformed version of Zitterbewegung in relativistic quantum dynamics and (ii) calculated the partition function and all thermal quantities such as the free energy, total energy, entropy, and specific heat. The extension to the case of Graphene has been discussed only in the case of a pure phase (q=eiη).

scholarly journals Transition from one- to two-dimensional development facilitates maintenance of multicellularity

2016 ◽  
Vol 3 (9) ◽  
pp. 160554
Author(s):  
Alejandra M. Manjarrez-Casas ◽  
Homayoun C. Bagheri ◽  
Akos Dobay
Keyword(s):  
Cell Division ◽  
Turnover Rate ◽  
Large Cell ◽  
Life Cycles ◽  
Two Dimensions ◽  
Developmental Cycle ◽  
Two Dimensional ◽  
Multicellular Development ◽  
The One ◽  
Multicellular Organisms

Filamentous organisms represent an example where incomplete separation after cell division underlies the development of multicellular formations. With a view to understanding the evolution of more complex multicellular structures, we explore the transition of multicellular growth from one to two dimensions. We develop a computational model to simulate multicellular development in populations where cells exhibit density-dependent division and death rates. In both the one- and two-dimensional contexts, multicellular formations go through a developmental cycle of growth and subsequent decay. However, the model shows that a transition to a higher dimension increases the size of multicellular formations and facilitates the maintenance of large cell clusters for significantly longer periods of time. We further show that the turnover rate for cell division and death scales with the number of iterations required to reach the stationary multicellular size at equilibrium. Although size and life cycles of multicellular organisms are affected by other environmental and genetic factors, the model presented here evaluates the extent to which the transition of multicellular growth from one to two dimensions contributes to the maintenance of multicellular structures during development.

scholarly journals BELLS GALORE: OSCILLATIONS AND CIRCLE-MAP DYNAMICS FROM SPACE-FILLING FRACTAL FUNCTIONS

Fractals ◽  
2008 ◽  
Vol 16 (04) ◽  
pp. 367-378 ◽  
Author(s):  
CARLOS E. PUENTE ◽  
ANDREA CORTIS ◽  
BELLIE SIVAKUMAR
Keyword(s):  
Two Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Circle Map ◽  
Space Filling ◽  
Affine Mappings ◽  
Oscillatory Pattern ◽  
Fractal Functions ◽  
The Many ◽  
The One

The construction of a host of interesting patterns over one and two dimensions, as transformations of multifractal measures via fractal interpolating functions related to simple affine mappings, is reviewed. It is illustrated that, while space-filling fractal functions most commonly yield limiting Gaussian distribution measures (bells), there are also situations (depending on the affine mappings' parameters) in which there is no limit. Specifically, the one-dimensional case may result in oscillations between two bells, whereas the two-dimensional case may give rise to unexpected circle map dynamics of an arbitrary number of two-dimensional circular bells. It is also shown that, despite the multitude of bells over two dimensions, whose means dance making regular polygons or stars inscribed on a circle, the iteration of affine maps yields exotic kaleidoscopes that decompose such an oscillatory pattern in a way that is similar to the many cases that converge to a single bell.

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