scholarly journals Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models

2020 ◽  
Vol 102 (10) ◽  
Author(s):  
Elena Medina ◽  
Luis Martínez Alonso
Keyword(s):  
Jacobi Formulation

Hamilton–Jacobi Treatment of Lagrangians with Linear Velocities

2003 ◽  
Vol 18 (23) ◽  
pp. 1591-1596 ◽  
Author(s):  
Eqab M. Rabei ◽  
Khaled I. Nawafleh ◽  
Yacoub S. Abdelrahman ◽  
H. Y. Rashed Omari
Keyword(s):  
Equations Of Motion ◽  
Lagrangian Systems ◽  
New Approach ◽  
Consistency Conditions ◽  
Action Integral ◽  
Jacobi Formulation

A new approach for solving mechanical problems of Linear Lagrangian systems using the Hamilton–Jacobi formulation is proposed. The equations of motion are recovered from the action integral. It has been proved that there is no need to follow the consistency conditions of the Dirac approach.

scholarly journals The Hamilton-Jacobi equation and holographic renormalization group flows on sphere

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Nakwoo Kim ◽  
Se-Jin Kim
Keyword(s):  
Renormalization Group ◽  
Characteristic Function ◽  
Jacobi Equation ◽  
Degrees Of Freedom ◽  
Warp Factor ◽  
Holographic Renormalization ◽  
Mass Terms ◽  
Renormalization Group Flows ◽  
Jacobi Formulation ◽  
Hamilton Jacobi Equation

Abstract We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton’s characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.

Hamilton–Jacobi Formulation for Systems in Terms of Riesz’s Fractional Derivatives

2011 ◽  
Vol 50 (5) ◽  
pp. 1569-1576 ◽  
Author(s):  
Eqab M. Rabei ◽  
Ibrahim M. Rawashdeh ◽  
Sami Muslih ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivatives ◽  
Jacobi Formulation
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