Hamilton–Jacobi Approach to Berezinian Singular Systems

Abstract

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the HamiltonJacobi equation for such systems, analizing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared.

Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis

“…The hamiltonian densities H and H 0 a are related to the parameters x 0 and λ a , respectively. In order to test the ICs for (17) we define the fundamental Poisson…”

“…The completeness of this set is assured by the Frobenius' theorem, which implies that the hamiltonians must obey a set of integrability conditions. To better understand this formalism, several improvements [16][17][18][19][20] and applications [21][22][23][24][25][26] have been made. One of the desired features of the HJ formalism is the fact that no analogue of Dirac's conjecture is needed.…”

Formalismo de Hamilton-Jacobi à la Carathéodory

“…Os primeiros trabalhos estendendo a formulação desenvolvida por Carathéodory para o tratamento de sistemas singulares foram feitos por Güler em 1992 [15,16]. Outras extensões foram realizadas por outros autores e, hoje,é bem estabelecido como são descritos em HJ os sistemas singulares com derivadas de ordem superior a um [24,25], sistemas singulares descritos por variáveis de Berezin [26], sistemas descritos por ações de primeira ordem [27], entre outros. Desde o desenvolvimento inicial feito por Güler, diversas aplicações a sistemas singulares têm sido realizadas [17][18][19][20][21][22][23], provendo um novo olhar no estudo de sistemas singulares.…”

Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

“…The Hamilton-Jacobi formalism (HJ) based on Carathéodory's idea [15] has gained a considerable importance during the last decade due to its various applications to quantization of constrained systems [16].…”

“…[16][17][18][19][20][21][22][23] and the references therein). The starting point of this method is a singular Lagrangian L. In this approach we use the initial canonical Hamiltonian H 0 and all primary constraints denoted by H α .…”