Symplectic Embedding and Hamilton–jacobi Analysis of Proca Model

Abstract

Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess-Zumino and gauge fixing terms of BRST invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton-Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.

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

“…(18). With the complete set of involutive hamiltonians of the system the dynamics in instant-form is given by the fundamental differential (21), and the characteristic equations of the system, (22), follow. The temporal part of the dynamics is shown to be equivalent to the field equation, while the dynamics along the parameters λ a and ω a are considered as canonical transformations whose generator is given by (26).…”

“…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.…”

From massive self-dual p-forms towards gauge p-forms

“…We observe that the constraints (23) and (25) generate a second-class constraints subset. Eliminating the second-class constraints (23) and (25) ) we are left with a system subject to the second-class constraints (24) and (26) …”

“…The construction of the equivalent first-class system can be achieved using the gauge unfixing [2][3][4][5][6] or constraints conversion [7][8][9][10][11] methods. This quantization procedure has been applied to various models [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Formalismo de Hamilton-Jacobi à la Carathéodory

“…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. …”