SCALE AND CONFORMAL INVARIANCE AND VARIATION OF THE METRIC

2006 ◽  
Vol 21 (17) ◽  
pp. 3641-3647 ◽  
Author(s):  
J. SADEGHI ◽  
A. TOFIGHI ◽  
A. BANIJAMALI
Keyword(s):  
Conformal Invariance ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conserved Currents

We consider the relation between scale invariance and conformal invariance. In our analysis the variation of the metric is taken into account. By imposing some conditions on the trace of the energy–momentum tensor and on the variation of the action, we find that the scale dimensions of the fields are not affected. We also obtain the conserved currents. We find that the conditions for conformal invariance are stronger than for scale invariance.

scholarly journals TODA FIELD THEORIES ASSOCIATED WITH HYPERBOLIC KAC-MOODY ALGEBRA — PAINLEVÉ PROPERTIES AND W ALGEBRAS

1996 ◽  
Vol 11 (31) ◽  
pp. 5479-5493 ◽  
Author(s):  
REINHOLD W. GEBERT ◽  
SHUN’YA MIZOGUCHI ◽  
TAKEO INAMI
Keyword(s):  
Lie Algebras ◽  
Energy Momentum Tensor ◽  
Direct Calculation ◽  
Momentum Tensor ◽  
Field Theories ◽  
Painlevé Analysis ◽  
Painlevé Test ◽  
Moody Algebra ◽  
Simple Lie Algebras ◽  
Conserved Currents

We show that the Painlevé test is useful not only for probing (non)integrability but also for finding the values of spins of conserved currents (W currents) in Toda field theories (TFT’s). In the case of TFT’s based on simple Lie algebras the locations of resonances are shown to give precisely the spins of conserved W currents. We apply this test to TFT’s based strictly on hyperbolic Kac-Moody algebras and show that there exist no resonance other than that at n = 2, which corresponds to the energy-momentum tensor, indicating their nonintegrability. We also check by direct calculation that there are no spin-3 or -4 conserved currents for all the hyperbolic TFT’s in agreement with the result of our Painlevé analysis.

Scale invariance and the energy–momentum tensor

1970 ◽  
Vol 48 (20) ◽  
pp. 2371-2375
Author(s):  
Peter Bendix
Keyword(s):  
Gravitational Field ◽  
Scale Invariance ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Scale Invariant ◽  
New Energy ◽  
Klein Gordon

A method is described by which an energy–momentum tensor can be constructed such that in addition to the usual properties of this tensor it acquires the property of scale invariance in the absence of masses and charges. (The new energy–momentum tensor constructed here is not the source of the gravitational field, however.) It is shown that the usual construction for the massless Klein–Gordon field yields an energy–momentum tensor which is not scale invariant, whereas using the construction described here, one finds a scale invariant energy–momentum tensor for this case.

THE ALGEBRA OF THE ENERGY-MOMENTUM TENSOR AND THE NOETHER CURRENTS IN OFF-CRITICAL WZNW MODELS

1993 ◽  
Vol 08 (09) ◽  
pp. 803-809
Author(s):  
M. FORGER ◽  
J. LAARTZ
Keyword(s):  
Current Algebra ◽  
Conformal Invariance ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Momentum Tensor ◽  
Global Symmetry ◽  
Composite Field ◽  
Derivatives Of ◽  
Algebra Part

The recently derived current algebra of classical principal chiral models with a Wess-Zumino term is extended to include the energy-momentum tensor. It is found that the energy-momentum tensor θµν, the Noether currents [Formula: see text] and [Formula: see text] associated with the global symmetry of the theory and the composite field t appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of [Formula: see text] and t, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge c=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are a deformation of the usual affine Kac-Moody/Sugawara construction.

SPONTANEOUS BREAKING OF SCALE INVARIANCE AND SUPERSYMMETRIC MODELS AT FINITE TEMPERATURE

2005 ◽  
Vol 20 (19) ◽  
pp. 4475-4483 ◽  
Author(s):  
Joshua Feinberg ◽  
Moshe Moshe ◽  
Michael Smolkin ◽  
Jean Zinn-Justin
Keyword(s):  
Finite Temperature ◽  
Phase Structure ◽  
Scale Invariance ◽  
Bound States ◽  
Energy Momentum Tensor ◽  
Goldstone Boson ◽  
Critical Value ◽  
Momentum Tensor ◽  
Spontaneous Breaking ◽  
Symmetric Model

The phase structure of a supersymmetric, vector O(N) symmetric model at Large N in three dimension is presented. At zero temperature it reveals spontaneous breaking of scale invariance with no explicit breaking. When the attracting force between the massive quanta, bosons and fermions, is tuned to a certain critical value one finds massless bound states, a Goldstone boson and a Goldstone fermion, associated with the spontaneous breaking of scale invariance (massless dilaton and dilatino). The effect of finite temperature on this phenomenon is elucidated. Expectation values of the energy momentum tensor are calculated at zero and finite temperatures. The phase structure is unveiled in the limit N → ∞. We point out that at a certain critical value of the coupling constant the trace of the energy momentum tensor vanishes at all temperatures.

scholarly journals Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 70
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Cosmo ◽  
Alberto Ibort ◽  
Giuseppe Marmo ◽  
Luca Schiavone ◽  
...  
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Embedding Theorem ◽  
Tensor Algebra ◽  
Poisson Brackets ◽  
Momentum Map ◽  
First Order ◽  
Klein Gordon ◽  
Presymplectic Structure ◽  
Conserved Currents

As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt with by using a symplectic regularization based on an application of Gotay’s coisotropic embedding theorem. An analysis of electrodynamics and of the Klein–Gordon theory illustrate the main results of the theory as well as the emergence of the energy–momentum tensor algebra of conserved currents.

scholarly journals On Sugawara construction on celestial sphere

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Wei Fan ◽  
Angelos Fotopoulos ◽  
Stephan Stieberger ◽  
Tomasz R. Taylor
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Conformal Transformations ◽  
Moody Algebra ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Conformal Field ◽  
Celestial Sphere ◽  
Double Copy ◽  
Conserved Currents

Abstract Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.

Conserved currents of the Klein–Gordon field

1981 ◽  
Vol 90 (3) ◽  
pp. 507-515 ◽  
Author(s):  
T. J. Gordon
Keyword(s):  
Field Theory ◽  
Energy Momentum Tensor ◽  
Differential Forms ◽  
Momentum Tensor ◽  
Mathematical Background ◽  
Poincaré Lemma ◽  
Klein Gordon ◽  
Countably Infinite ◽  
Infinite Set ◽  
Conserved Currents

AbstractA method is presented whereby all locally defined conserved currents of the Klein-Gordon field are found. The mathematical background to the method includes a generalization of the Poincaré lemma of the calculus of exterior differential forms. It is found that the only conserved currents are essentially a countably infinite set of functions, bilinear in the field, together with a single current in the case where the mass is zero. The usual energy-momentum tensor is included amongst these functions. The method does not depend on the use of any canonical formulation of the field theory.

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