2,244 research outputs found
Covariant canonical formalism for Dirac-Nambu-Goto bosonic p-branes and the Gauss-Bonnet topological term in string theory
Using a covariant and gauge invariant geometric structure constructed on the
Witten covariant phase space for Dirac-Nambu-Goto bosonic p-branes propagating
in a curved background, we find the canonically conjugate variables, and the
relevant commutation relations are considered, as well as, we find the
canonical variables for the Gauss-Bonnet topological term in string theory.Comment: 8 page
Basic symplectic geometry for p-branes with thickness in a curved background
We show that the Witten covariant phase space for p-branes with thickness in
an arbitrary background is endowed of a symplectic potential, which although is
not important to the dynamics of the system, plays a relevant role on the phase
space, allowing us to generate a symplectic structure for the theory and
therefore give a covariant description of canonical formalism for quantization.Comment: 15 pages. To be published in Journal Modern Physics Letters
Poincar\'e charges for chiral membranes
Using basic ideas of simplectic geometry, we find the covariant canonically
conjugate variables, the commutation relations and the Poincar\'e charges for
chiral superconducting membranes (with null currents), as well as we find the
stress tensor for the theory under study.Comment: 13 page
Simplectic geometry and the canonical variables for Dirac-Nambu-Goto and Gauss-Bonnet system in string theory
Using a strongly covariant formalism given by Carter for the deformations
dynamics of p-branes in a curved background and a covariant and gauge invariant
geometric structure constructed on the corresponding Witten's phase space, we
identify the canonical variables for Dirac-Nambu-Goto [DNG] and Gauss-Bonnet
[GB] system in string theory. Future extensions of the present results are
outlined.Comment: 12 page
Hamiltonian dynamics of 5D Kalb-Ramond theories with a compact dimension
A detailed Hamiltonian analysis for a five-dimensional Kalb-Ramond, massive
Kalb-Ramond and St{\"{u}}eckelberg Kalb-Ramond theories with a compact
dimension is performed. We develop a complete constraint program, then we
quantize the theory by constructing the Dirac brackets. From the gauge
transformations of the theories, we fix a particular gauge and we find
pseudo-Goldstone bosons in Kalb-Ramond and St{\"{u}}eckelberg Kalb-Ramond's
effective theories. Finally we discuss some remarks and prospects
A pure Dirac's method for Husain-Kuchar theory
A pure Dirac's canonical analysis, defined in the full phase space for the
Husain-Kuchar model is discussed in detail. This approach allows us to
determine the extended action, the extended Hamiltonian, the complete
constraint algebra and the gauge transformations for all variables that occur
in the action principle. The complete set of constraints defined on the full
phase space allow us to calculate the Dirac algebra structure of the theory and
a local weighted measure for the path integral quantization method. Finally, we
discuss briefly the necessary mathematical structure to perform the canonical
quantization program within the framework of the loop quantum gravity approach
A pure Dirac's method for Yang-Mills expressed as a constrained BF-like theory
A pure Dirac's method of Yang-Mills expressed as a constrained BF-like theory
is performed. In this paper we study an action principle composed by the
coupling of two topological BF-like theories, which at the Lagrangian level
reproduces Yang-Mills equations. By a pure Dirac's method we mean that we
consider all the variables that occur in the Lagrangian density as dynamical
variables and not only those ones that involve temporal derivatives. The
analysis in the complete phase space enable us to calculate the extended
Hamiltonian, the extended action, the constraint algebra, the gauge
transformations and then we carry out the counting of degrees of freedom. We
show that the constrained BF-like theory correspond at classical level to
Yang-Mills theory. From the results obtained, we discuss briefly the
quantization of the theory. In addition we compare our results with
alternatives models that have been reported in the literatur
The Hamilton-Jacobi analysis and Canonical Covariant description for three dimensional Palatini theory plus a Chern-Simons term
By using the Hamilton-Jacobi [HJ] framework the three dimensional Palatini
theory plus a Chern-Simons term [PCS] is analyzed. We report the complete set
of Hamiltonians and a generalized differential from which all
symmetries of the theory are identified. Moreover, we show that in spite of PCS
Lagrangian produces Einstein's equations, the generalized brackets depend
on a Barbero-Immirzi like parameter. In addition we complete our study by
performing a canonical covariant analysis, and we construct a closed and gauge
invariant two form that encodes the symplectic geometry of the covariant phase
space
Hamiltonian Dynamics for an alternative action describing Maxwell's equations
We develop a complete Dirac's canonical analysis for an alternative action
that yields Maxwell's four-dimensional equations of motion. We study in detail
the full symmetries of the action by following all steps of Dirac's method in
order to obtain a detailed description of symmetries. Our results indicate that
such an action does not have the same symmetries than Maxwell theory, namely,
the model is not a gauge theory and the number of physical degrees of freedom
are different
Faddeev-Jackiw quantization of four dimensional BF theory
The symplectic analysis of a four dimensional theory in the context of
the Faddeev-Jackiw symplectic approach is performed. It is shown that this
method is more economical than Dirac's formalism. In particular, the complete
set of Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets
are reported. In addition, we show that the generalized Faddeev-Jackiw brackets
and the Dirac ones coincide to each other. Finally, the similarities and
advantages between Faddeev-Jackiw method and Dirac's formalism are briefly
discussed
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