Legendre-Transformation

Physik Online ◽  
2018 ◽  
Author(s):  
Karl Schilcher
2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.


1995 ◽  
Vol 121 ◽  
pp. 1-428 ◽  
Author(s):  
Reijiro Fukuda ◽  
Masahiro Komachiya ◽  
Satoshi Yokojima ◽  
Yoko Suzuki ◽  
Ko Okumura ◽  
...  

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 163
Author(s):  
Dana Smetanová

The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton equations and the Euler–Lagrange equations are studied. The theory is illustrated on examples of Hamiltonian systems satisfying the following conditions: (a) the Hamiltonian system is strongly regular and the Legendre transformation exists; (b) the Hamiltonian system is strongly regular and the Legendre transformation does not exist; (c) the Legendre transformation exists and the Hamiltonian system is not regular but satisfies a weaker condition.


2019 ◽  
Vol 16 (supp02) ◽  
pp. 1941006
Author(s):  
Layth M. Alabdulsada ◽  
László Kozma

A sub-Finslerian manifold is, roughly speaking, a manifold endowed with a Finsler type metric which is defined on a [Formula: see text]-dimensional smooth distribution only, not on the whole tangent manifold. Our purpose is to construct a generalized nonlinear connection for a sub-Finslerian manifold, called [Formula: see text]-connection by the Legendre transformation which characterizes normal extremals of a sub-Finsler structure as geodesics of this connection. We also wish to investigate some of its properties like normal, adapted, partial and metrical.


1967 ◽  
Vol 19 ◽  
pp. 200-205 ◽  
Author(s):  
R. T. Rockafellar

Fenchel's conjugate correspondence for convex functions may be viewed as a generalization of the classical Legendre correspondence, as indicated briefly in (6). Here the relationship between the two correspondences will be described in detail. Essentially, the conjugate reduces to the Legendre transform if and only if the subdifferential of the convex function is a one-to-one mapping. The one-to-oneness is equivalent to differentiability and strict convexity, plus a condition that the function become infinitely steep near boundary points of its effective domain. These conditions are shown to be the very ones under which the Legendre correspondence is well-defined and symmetric among convex functions. Facts about Legendre transforms may thus be deduced using the elegant, geometrically motivated methods of Fenchel. This has definite advantages over the more restrictive classical treatment of the Legendre transformation in terms of implicit functions, determinants, and the like.


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