76 research outputs found
Non-Involutive Constrained Systems and Hamilton-Jacobi Formalism
In this work we discuss the natural appearance of the Generalized Brackets in
systems with non-involutive (equivalent to second class) constraints in the
Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of
the integrability conditions leads to the reduction of degrees of freedom of
these systems and, as consequence, naturally defines a dynamics in a reduced
phase space.Comment: 12 page
Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method
The Hamilton-Jacobi analysis is applied to the dynamics of the scalar
fluctuations about the Friedmann-Robertson-Walker (FRW). The gauge conditions
are found from the consistency conditions. The physical degrees of freedom of
the model are obtain by symplectic projector method. The role of the linearly
dependent Hamiltonians and the gauge variables in Hamilton-Jacobi formalism is
discussed.Comment: 11 page
Hamilton-Jacobi Approach for First Order Actions and Theories with Higher Derivatives
In this work we analyze systems described by Lagrangians with higher order
derivatives in the context of the Hamilton-Jacobi formalism for first order
actions. Two different approaches are studied here: the first one is analogous
to the description of theories with higher derivatives in the hamiltonian
formalism according to [Sov. Phys. Journ. 26 (1983) 730; the second treats the
case where degenerate coordinate are present, in an analogy to reference [Nucl.
Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison
between both approaches is made
General Relativity in two dimensions: a Hamilton-Jacobi constraint analysis
We will analyze the constraint structure of the Einstein-Hilbert first-order
action in two dimensions using the Hamilton-Jacobi approach. We will be able to
find a set of involutive, as well as a set of non-involutive constraints. Using
generalized brackets we will show how to assure integrability of the theory, to
eliminate the set of non-involutive constraints, and to build the field
equations
Remarks on Duffin-Kemmer-Petiau theory and gauge invariance
Two problems relative to the electromagnetic coupling of Duffin-Kemmer-Petiau
(DKP) theory are discussed: the presence of an anomalous term in the
Hamiltonian form of the theory and the apparent difference between the
Interaction terms in DKP and Klein-Gordon (KG) Lagrangians. For this, we first
discuss the behavior of DKP field and its physical components under gauge
transformations. From this analysis, we can show that these problems simply do
not exist if one correctly analyses the physical components of DKP field.Comment: 19 pages, no figure
Hamilton-Jacobi approach to Berezinian singular systems
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 Hamilton-Jacobi 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.Comment: LaTex, 30 pages, no figure
Faddeev-Jackiw quantization of Proca Electrodynamics
The generalized symplectic formalism quantization method is employed to study the gauge invariance Proca electrodynamics theory. We show that the zero modes of the symplectic matrix are the generators of the gauge transformation. After fixing the gauge, the generalized brackets are calculated
Remarks on Infrared Dynamics in QED3
In this work we study how the infrared sector of the interaction Hamiltonian
can affect the construction of the S matrix operator of QED in (2+1)
dimensions.Comment: 9 page
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