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Hamilton-Jacobi Theory in k-Symplectic Field Theories  [PDF]
M. De León,D. Martín De Diego,J. C. Marrero,M. Salgado,S. Vilari?o
Physics , 2010, DOI: 10.1142/S0219887810004919
Abstract: In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework.
A Geometric Hamilton-Jacobi Theory for Classical Field Theories  [PDF]
M. de Leon,J. C. Marrero,D. Martin de Diego
Physics , 2008,
Abstract: In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.
Hamilton-Jacobi theory in k-cosymplectic field theories  [PDF]
M. de León,S. Vilari?o
Physics , 2013, DOI: 10.1142/S0219887814500078
Abstract: In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.
Unified formalism for the generalized kth-order Hamilton-Jacobi problem  [PDF]
Leonardo Colombo,Manuel de León,Pedro D. Prieto-Martínez,Narciso Román-Roy
Physics , 2013, DOI: 10.1142/S0219887814600378
Abstract: The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.
Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories  [PDF]
Wulf Boettger,Henning Wissowski,Hans A. Kastrup
Physics , 1995,
Abstract: The Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and $\phi^4$ theories. For simplicity we use the Hamilton--Jacobi equation of DeDonder and Weyl. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations between Hamilton--Jacobi wave fronts and the corresponding families of extremals embedded therein. B\"acklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs.
Hamilton-Jacobi formalism for Linearized Gravity  [PDF]
M. C. Bertin,B. M. Pimentel,C. E. Valcárcel,G. E. R. Zambrano
Physics , 2011, DOI: 10.1088/0264-9381/28/17/175015
Abstract: In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.
Energy Eigenvalues For Supersymmetric Potentials via Quantum Hamilton-Jacobi Formalism  [PDF]
R. S. Bhalla,A. K. Kapoor,P. K. Panigrahi
Physics , 1995,
Abstract: Using quantum Hamilton-Jacobi formalism of Leacock and Padgett, we show how to obtain the exact eigenvalues for supersymmetric (SUSY) potentials.
On the Hamilton-Jacobi formalism for fermionic systems  [PDF]
C. Ramírez,P. A. Ritto
Physics , 2003,
Abstract: The Hamilton-Jacobi formalism for fermionic systems is studied. We derive the HJ equations from the canonical transformation procedure, taking into account the second class constraints typical of these systems. It is shown that these constraints ensure the consistency of the solution, according to the characteristics of fermionic systems. The explicit solutions for simple examples are computed. Some aspects related to canonical transformations and to quantization are discussed.
A Hamilton-Jacobi Formalism for Thermodynamics  [PDF]
S. G. Rajeev
Mathematics , 2007, DOI: 10.1016/j.aop.2007.12.007
Abstract: We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is (2n+1)-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The `time' variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.
Geometric Hamilton-Jacobi Field Theory  [PDF]
Luca Vitagliano
Mathematics , 2011, DOI: 10.1142/S0219887812600080
Abstract: I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
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