scholarly journals Conservation laws and variational sequences in gauge-natural theories

2001 ◽  
Vol 130 (3) ◽  
pp. 555-569 ◽  
Author(s):  
L. FATIBENE ◽  
M. FRANCAVIGLIA ◽  
M. PALESE
Keyword(s):  
Conservation Laws ◽  
General Setting ◽  
Symmetric Tensor ◽  
Field Theories ◽  
Lie Derivative ◽  
Derivative Operator ◽  
Tensor Density ◽  
Conserved Currents ◽  
Natural Bundle ◽  
Suitable Vector

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable vector density is known to generate the so-called conserved Noether currents. It turns out that along any section of the relevant gauge-natural bundle this density is the divergence of a skew-symmetric tensor density, which is called a superpotential for the conserved currents.We describe gauge-natural superpotentials in the framework of finite order variational sequences according to Krupka. We refer to previous results of ours on variational Lie derivatives concerning abstract versions of Noether's theorems, which are here interpreted in terms of ‘horizontal’ and ‘vertical’ conserved currents. The gauge-natural lift of principal automorphisms implies suitable linearity properties of the Lie derivative operator. Thus abstract results due to Kolář, concerning the integration by parts procedure, can be applied to prove the existence and globality of superpotentials in a very general setting.

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

Perturbations of conservation laws in field theories

1986 ◽  
Vol 167 (2) ◽  
pp. 354-389 ◽  
Author(s):  
Judith M Arms ◽  
Ian M Anderson
Keyword(s):  
Conservation Laws ◽  
Field Theories

scholarly journals QUANTUM INTEGRABILITY OF COUPLED N=1 SUPER SINE/SINH–GORDON THEORIES AND THE LIE SUPERALGEBRA D(2,1;α)

1999 ◽  
Vol 14 (16) ◽  
pp. 2551-2580 ◽  
Author(s):  
JONATHAN M. EVANS ◽  
JENS OLE MADSEN
Keyword(s):  
Quantum Theory ◽  
Lie Superalgebra ◽  
Field Theories ◽  
Continuous Family ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Classical Level ◽  
Quantum Integrability ◽  
Integrable Quantum ◽  
Conserved Currents

We discuss certain integrable quantum field theories in 1+1 dimensions consisting of coupled sine/sinh–Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra D(2,1;α)(1) (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter α. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.

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.

scholarly journals USING CONSERVATION LAWS TO SOLVE TODA FIELD THEORIES

1996 ◽  
Vol 11 (10) ◽  
pp. 1831-1853 ◽  
Author(s):  
ERLING G.B. HOHLER ◽  
KÅRE OLAUSSEN
Keyword(s):  
Field Theory ◽  
Differential Equations ◽  
Conservation Laws ◽  
Closed System ◽  
Transformation Group ◽  
Field Theories ◽  
Real Form ◽  
Local Conservation ◽  
Considerable Detail ◽  
Toda Field Theory

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be used to solve it. We show that for models where the conservation laws can be written in one-sided forms, [Formula: see text] like the problem can always be reduced to solving a closed system of ordinary differential equations. We investigate the A1, A2 and B2 Toda field theories in considerable detail from this viewpoint. One of our findings is that there is in each case a transformation group intrinsic to the model. This group is built on a specific real form of the Lie algebra used to label the Toda field theory. It is the group of field transformations which leaves the conserved densities invariant.

BOUND STATE ENERGIES IN THE 1/N EXPANSION

1993 ◽  
Vol 08 (09) ◽  
pp. 1613-1628
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Bound States ◽  
Symmetric Tensor ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
3 Dimensional ◽  
Weakly Coupled

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

scholarly journals Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

2019 ◽  
Vol 16 (03) ◽  
pp. 1950049
Author(s):  
Marcella Palese ◽  
Ekkehart Winterroth
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Higgs Field ◽  
Field Theories ◽  
Conserved Quantities ◽  
Principal Bundles ◽  
Yang Mills ◽  
Covariant Gauge ◽  
Higgs Fields ◽  
Natural Bundle

We address some new issues concerning spontaneous symmetry breaking. We define classical Higgs fields for gauge-natural invariant Yang–Mills type Lagrangian field theories through the requirement of the existence of canonical covariant gauge-natural conserved quantities. As an illustrative example, we consider the ‘gluon Lagrangian’, i.e. a Yang–Mills Lagrangian on the [Formula: see text]-order gauge-natural bundle of [Formula: see text]-principal connections, and canonically define a ‘gluon’ classical Higgs field through the split reductive structure induced by the kernel of the associated gauge-natural Jacobi morphism.

Sign in / Sign up

Export Citation Format

Share Document