Conformal symmetry in two-dimensional space: Recursion representation of conformal block

1987 ◽  
Vol 73 (1) ◽  
pp. 1088-1093 ◽  
Author(s):  
Al. B. Zamolodchikov
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Conformal Block ◽  
Two Dimensional

scholarly journals Conformal Symmetry and Supersymmetry in Rindler Space

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 144
Author(s):  
Jan-Willem van Holten
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Extended Space ◽  
Rindler Space ◽  
Dimensional Space Time ◽  
Critical Spectrum ◽  
Infinite Strings ◽  
Bogoliubov Transformations

This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional space-time. Generically, in addition to a conformal co-ordinate transformation, the transformation of fields from Minkowski to Rindler space is accompanied by local conformal and Lorentz transformations of the components, which also affect the Bogoliubov transformations between the associated Fock spaces. I construct these transformations for massless scalars and spinors, as well as for the ghost and super-ghost fields necessary in theories with local conformal and supersymmetries, as arising from coupling to two-dimensional (2-D) gravity or supergravity. Cancellation of the anomalies in Minkowski and in Rindler space requires theories with the well-known critical spectrum of particles that arise in string theory in the limit of infinite strings, and it is relevant for the equivalence of Minkowski and Rindler frame theories.

METHOD OF SOLVING CONFORMAL MODELS IN D-DIMENSIONAL SPACE III SECONDARY FIELDS IN D>2 AND THE SOLUTION OF TWO-DIMENSIONAL MODELS

1998 ◽  
Vol 13 (28) ◽  
pp. 4837-4888
Author(s):  
E. S. FRADKIN ◽  
M. YA. PALCHIK
Keyword(s):  
Hilbert Space ◽  
Dimensional Space ◽  
Conformal Symmetry ◽  
Solvable Model ◽  
Virasoro Algebra ◽  
Green Functions ◽  
Two Dimensional ◽  
Ward Identities ◽  
Fundamental Field ◽  
Conformal Models

We proceed with the study (started in Refs. 1 and 2) of the Hilbert space of conformal field theory in D di mensions. We discuss an infinite family of secondary fields [Formula: see text] generated by the action of the components of energy–momentum tensor Tμν on the fundamental (primary) field. It is shown that the states of these fields form a specific sector of the Hilbert space H which is determined by the Ward identities and [Formula: see text]-dimensional conformal symmetry. We demonstrate that for D = 2 the subspace H coincides with the space of representation of the Virasoro algebra. Each exactly solvable model in the case of D ≥ 2 is defined by the requirement of vanishing of a certain state Qs(x)|0> ⊂ H analogous to the null vector of two-dimensional theory. The Green functions of the fields [Formula: see text] are calculated in terms of the Green functions of the fundamental field. It is shown that all the Green functions of the type [Formula: see text] satisfy the anomalous Ward identities. The anomalous contributions are given by the fields [Formula: see text], where s′≤s-1. The fields Qs are constructed as superpositions of secondary fields with the anomalous contribution equal to zero, An approach developed is based on a finite-dimensional conformal symmetry for any D ≥ 2. Nevertheless the resulting models have the structure analogous to that of two-dimensional conformal theories. This analogy is discussed in detail. It is shown that for D = 2 the family of models coincides with the well-known family of conformal models based on infinite-dimensional conformal symmetry. The analysis of this phenomenon indicates the existence of the D-dimensional analog of the Virasoro algebra.

ACTION PRINCIPLE, VIRASORO STRUCTURE AND ANALYTICITY IN NONPERTURBATIVE TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (17) ◽  
pp. 4015-4038 ◽  
Author(s):  
TAMIAKI YONEYA
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Scaling Limit ◽  
Closed String ◽  
Action Principle ◽  
String Equation ◽  
Two Dimensional ◽  
Polynomial Potential ◽  
Symmetry Properties ◽  
Dimensional Gravity

The consequences of symmetry properties of a previously proposed action principle which describes the theory space of two-dimensional gravity are investigated. The string equation corresponding to the double scaling limit of the one-matrix model with general polynomial potential is expressed as a bilinear equation for the τ function of the KP hierarchy. The Virasoro condition for the τ function is then shown to be a Ward-like identity derived from the string equation corresponding to a conformal symmetry of the action principle. The possibility of a Ginzburg-Landau type integral representation of the τ function as a version of noncritical closed string field theory in less-than-one-dimensional space-time is discussed. Finally, the role of analyticity with respect to the eigenvalue of the puncture operator in interpreting the action principle is emphasized.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

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.

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