scholarly journals NON-COMMUTATIVE EINSTEIN EQUATIONS AND SEIBERG–WITTEN MAP

2011 ◽  
Vol 03 ◽  
pp. 143-149 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Field Theory ◽  
Einstein Equations ◽  
Action Functional ◽  
Field Equations ◽  
Commutative Field ◽  
First Order ◽  
Classical Geometry ◽  
Pure Gravity

The Seiberg–Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper, relying upon the pure-gravity form of the action functional considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein equations, and whether the Seiberg–Witten map can lead to a solution of such equations when the underlying classical geometry is Schwarzschild. We find that, if one first obtains the non-commutative field equations by varying the action of Ref. 2 with respect to all non-commutative fields, and then tries to solve these equations by expressing the non-commutative fields in terms of the commutative ones via Seiberg–Witten map, no solution of these equations can be obtained when the commutative background is Schwarzschild.

scholarly journals THE SEIBERG–WITTEN MAP FOR NON-COMMUTATIVE PURE GRAVITY AND VACUUM MAXWELL THEORY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350023 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
MARCO FIGLIOLIA ◽  
PATRIZIA VITALE
Keyword(s):  
Explicit Construction ◽  
Einstein Equations ◽  
Electromagnetic Potential ◽  
Field Equations ◽  
Maxwell Theory ◽  
Commutative Field ◽  
Yang Mills ◽  
First Order ◽  
Pure Gravity ◽  
Vacuum Solutions

In this paper the Seiberg–Witten map is first analyzed for non-commutative Yang–Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg–Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space–time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg–Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg–Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector.

scholarly journals A geometrical analysis of the field equations in field theory

2002 ◽  
Vol 29 (12) ◽  
pp. 687-699 ◽  
Author(s):  
A. Echeverría-Enríquez ◽  
M. C. Muñoz-Lecanda ◽  
N. Román-Roy
Keyword(s):  
Field Theory ◽  
Classical Field ◽  
Field Theories ◽  
Geometrical Analysis ◽  
Field Equations ◽  
First Order ◽  
Nonuniqueness Of Solutions ◽  
Lagrangian And Hamiltonian Formalisms ◽  
Classical Field Theories ◽  
Geometric Formulation

We give a geometric formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and nonuniqueness of solutions of these equations, as well as their integrability.

scholarly journals TELEPARALLEL LAGRANGE GEOMETRY AND A UNIFIED FIELD THEORY: LINEARIZATION OF THE FIELD EQUATIONS

2013 ◽  
Vol 10 (03) ◽  
pp. 1250092 ◽  
Author(s):  
M. I. WANAS ◽  
NABIL L. YOUSSEF ◽  
A. M. SID-AHMED
Keyword(s):  
Field Theory ◽  
Approximate Solution ◽  
Order Of Approximation ◽  
Unified Field Theory ◽  
Field Equations ◽  
First Order ◽  
Unified Field ◽  
Vertical Field ◽  
Geometric Objects ◽  
Linearized Theory

This paper is a natural continuation of our previous paper: "Teleparallel Lagrange geometry and a unified field theory, Class. Quantum Grav.27 (2010) 045005 (29 pp)". In this paper, we apply a linearization scheme on the field equations obtained in the above-mentioned paper. Three important results under the linearization assumption are accomplished. First, the vertical fundamental geometric objects of the EAP-space lose their dependence on the positional argument x. Secondly, our linearized theory in the Cartan-type case coincides with the GFT in the first-order of approximation. Finally, an approximate solution of the vertical field equations is obtained.

scholarly journals CONFORMAL INVARIANCE IN CLASSICAL FIELD THEORY

1994 ◽  
Vol 09 (03) ◽  
pp. 225-239
Author(s):  
D.R. GRIGORE
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrangian Formalism ◽  
Conformal Transformations ◽  
Action Functional ◽  
First Order ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Chern Simons

A geometric generalization of the first order Lagrangian formalism is used to analyze a conformal field theory for an arbitrary primary field. We require that the global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exist a “Chern-Simons” type Lagrangian for a conformally invariant Lagrangian theory.

scholarly journals A Field Theory with Curvature and Anticurvature

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
M. I. Wanas ◽  
Mona M. Kamal
Keyword(s):  
Field Theory ◽  
Free Space ◽  
Unified Field Theory ◽  
Field Equations ◽  
Weak Equivalence Principle ◽  
Unified Field ◽  
Special Cases ◽  
Geometric Objects ◽  
Pure Gravity ◽  
Physical Quantities

The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

scholarly journals Dissipation in the effective field theory for hydrodynamics: First-order effects

2013 ◽  
Vol 88 (10) ◽  
Author(s):  
Solomon Endlich ◽  
Alberto Nicolis ◽  
Rafael A. Porto ◽  
Junpu Wang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Order Effects ◽  
First Order

A UV complete picture of black hole conforming to low energy effective field theory

2018 ◽  
Vol 33 (36) ◽  
pp. 1850219
Author(s):  
Biplab Paik
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Effective Field Theory ◽  
Effective Field ◽  
Radiation Process ◽  
Quantum Black Hole ◽  
Classical Geometry ◽  
Characteristic Radius ◽  
Hole Geometry ◽  
Principle Of Causality

In this paper, we propose a UV complete, quantum improved picture of a black hole geometry that conforms to the IR gravity of effective field theory. Our work builds on identifying an effective space-distributed notion of black hole fluid in quantum improved regular Einstein gravity and its theoretical correspondence with a cosmology inspired power law fluctuation of matter. Hence, we make use of phenomenological asymptotic scales of matter fluctuation in static space to consequently derive a UV complete line-element of black hole space–time. In this appraisal, it gets explicit how principle of causality is preserved even while there is an effective spread of black hole fluid across horizon(s). Gravity changes from its conventional classical geometry-state to a quantum masked profile across a hypersurface of characteristic radius [Formula: see text]. We make analyses that probe the newly proposed quantum improved gravity in the contexts of regularity of Einstein fields, complete predictability of Hawking radiation process, and first law of black hole thermodynamics. It emerges that quantum black hole geometry self-regulates a regular timelike core that is abide by every quantum theoretical constraint while being flat around its center.

TWISTED POINCARE GROUP AND SPIN-STATISTICS

2005 ◽  
Vol 20 (27) ◽  
pp. 6268-6277 ◽  
Author(s):  
ALEKSANDR PINZUL
Keyword(s):  
Field Theory ◽  
Tensor Product ◽  
Poincaré Group ◽  
Commutative Field ◽  
Poincare Group ◽  
Quantized Fields

Recently it has been shown that it is possible to retain the Lorentz-invariant interpretation of the non-commutative field theory.1,2,3 This was achieved by the means of the twisted action of the Poincaré group on the tensor product of the fields. We investigate the consequences of this approach for the quantized fields.

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