Results 1  10
of
24
Covariant Theory of Asymptotic Symmetries, Conservation Laws and Central Charges
, 2001
"... Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters ar ..."
Abstract

Cited by 70 (13 self)
 Add to MetaCart
Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters are the parameters of gauge transformations that vanish suciently fast when evaluated at the background. A universal formula for asymptotically conserved n 2 forms in terms of the reducibility parameters is derived. Sucient conditions for niteness of the charges built out of the asymptotically conserved n 2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, YangMills theory and Einstein gravity where they reproduce familiar results.
On the Noether theorem for optimal control
 European Journal of Control
"... We extend Noether’s theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the conserved quantities previously obtained in the literature f ..."
Abstract

Cited by 23 (19 self)
 Add to MetaCart
We extend Noether’s theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the conserved quantities previously obtained in the literature for nonconservative problems of mechanics and the calculus of variations are derived.
Conservation Laws in Optimal Control
 In Dynamics, Bifurcations and Control
, 2002
"... Conservation laws, i.e. conserved quantities along EulerLagrange extremals, which are obtained on the basis of Noether's theorem, play an prominent role in mathematical analysis and physical applications. In this paper we present a general and constructive method to obtain conserved quantities alon ..."
Abstract

Cited by 14 (12 self)
 Add to MetaCart
Conservation laws, i.e. conserved quantities along EulerLagrange extremals, which are obtained on the basis of Noether's theorem, play an prominent role in mathematical analysis and physical applications. In this paper we present a general and constructive method to obtain conserved quantities along the Pontryagin extremals of optimal control problems, which are invariant under a family of transformations that explicitly change all (time, state, control) variables.
NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Lie point symmetries and first integrals: the Kowalevsky
, 2002
"... We show that Lie group analysis yields the first integrals admitted by any system of ordinary differential equations if the method developed by Nucci (J. Math. Phys. 37, 17721775 (1996)) is applied. As an example, we obtain the famous first integral of the Kowalevsky top. 1 ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We show that Lie group analysis yields the first integrals admitted by any system of ordinary differential equations if the method developed by Nucci (J. Math. Phys. 37, 17721775 (1996)) is applied. As an example, we obtain the famous first integral of the Kowalevsky top. 1
Singular dual pairs
, 2002
"... We generalize the notions of dual pair and polarity introduced by S. Lie [Lie90] and A. Weinstein [W83] in order to accommodate very relevant situations where the application of these ideas is desirable. The new notion of polarity is designed to deal with the loss of smoothness caused by the presenc ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We generalize the notions of dual pair and polarity introduced by S. Lie [Lie90] and A. Weinstein [W83] in order to accommodate very relevant situations where the application of these ideas is desirable. The new notion of polarity is designed to deal with the loss of smoothness caused by the presence of singularities that are encountered in many problems. We study in detail the relation between the newly introduced dual pairs, the quantum notion of Howe pair, and the symplectic leaf correspondence of Poisson manifolds in duality. The dual pairs arising in the context of symmetric Poisson manifolds are treated with special attention. We show that in this case and under very reasonable hypotheses we obtain a particularly well behaved kind of dual pairs that we call von Neumann pairs. Some of the ideas that we present in this paper shed some light on the optimal momentum maps introduced in [OR02a].
Pauli’s ideas on mind and matter in the context of contemporary science
 Journal of Consciousness Studies
, 2006
"... ..."
The Essential Harmony in the Classical Equations of Mathematical Physics
"... The possibility to transform any system of linear ordinary dierential equations into a system of constant coecient equations is demonstrated using Lie theory. Some examples relate the classical equations of mathematical physics to the simple harmonic oscillator. The r^oles of the third order for ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
The possibility to transform any system of linear ordinary dierential equations into a system of constant coecient equations is demonstrated using Lie theory. Some examples relate the classical equations of mathematical physics to the simple harmonic oscillator. The r^oles of the third order form of the ErmakovPinney equation and of Fleischenvon Weltunter systems are explained.
Lorenz integrable system moves à la Poinsot
, 2003
"... A transformation is derived which takes the Lorenz integrable system into the wellknown Euler equations of a torquefree rigid body about a fixed point, i.e. the famous motion à la Poinsot. The proof is based on Lie group analysis applied to two thirdorder ordinary differential equations admitting t ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
A transformation is derived which takes the Lorenz integrable system into the wellknown Euler equations of a torquefree rigid body about a fixed point, i.e. the famous motion à la Poinsot. The proof is based on Lie group analysis applied to two thirdorder ordinary differential equations admitting the same twodimensional Lie symmetry algebra. Lie’s classification of twodimensional symmetry algebras in the plane is used. If the same transformation is applied to the Lorenz system with any values of the parameters, then one obtains Euler equations of a rigid body about a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a threedimensional picture which looks like a “tornado ” the crosssection of which has a butterflyshape. Thus Lorenz’s butterfly has been transformed into a tornado.