103 research outputs found
Real sector of the nonminimally coupled scalar field to self-dual gravity
A scalar field nonminimally coupled to gravity is studied in the canonical
framework, using self-dual variables. The corresponding constraints are first
class and polynomial. To identify the real sector of the theory, reality
conditions are implemented as second class constraints, leading to three real
configurational degrees of freedom per space point. Nevertheless, this
realization makes non-polynomial some of the constraints. The original complex
symplectic structure reduces to the expected real one, by using the appropriate
Dirac brackets. For the sake of preserving the simplicity of the constraints,
an alternative method preventing the use of Dirac brackets, is discussed. It
consists of converting all second class constraints into first class by adding
extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure
The scalar sector in the Myers-Pospelov model
We construct a perturbative expansion of the scalar sector in the
Myers-Pospelov model, up to second order in the Lorentz violating parameter and
taking into account its higher-order time derivative character. This expansion
allows us to construct an hermitian positive-definite Hamiltonian which
provides a correct basis for quantization. Demanding that the modified normal
frequencies remain real requires the introduction of an upper bound in the
magnitude |k| of the momentum, which is a manifestation of the effective
character of the model. The free scalar propagator, including the corresponding
modified dispersion relations, is also calculated to the given order, thus
providing the starting point to consider radiative corrections when
interactions are introduced.Comment: Published in AIP Conf.Proc.977:214-223,200
An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator
Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator
using complex canonical transformations. We show that starting from a
Lagrangian approach we obtain a transformation that makes the extended PU
oscillator, with unequal frequencies, to be equivalent to two standard second
order oscillators which have the original number of degrees of freedom. Such
extension is provided by adding a total time derivative to the PU Lagrangian
together with a complexification of the original variables further subjected to
reality conditions in order to maintain the required number of degrees of
freedom. The analysis is accomplished at both the classical and quantum levels.
Remarkably, at the quantum level the negative norm states are eliminated, as
well as the problems of unbounded below energy and non-unitary time evolution.
We illustrate the idea of our approach by eliminating the negative norm states
in a complex oscillator. Next, we extend the procedure to the Pais-Uhlenbeck
oscillator. The corresponding quantum propagators are calculated using
Schwinger's quantum action principle. We also discuss the equal frequency case
at the classical level
An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator
Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with unequal frequencies, to be equivalent to two standard second order oscillators which have the original number of degrees of freedom. Such extension is provided by adding a total time derivative to the PU Lagrangian together with a complexification of the original variables further subjected to reality conditions in order to maintain the required number of degrees of freedom. The analysis is accomplished at both the classical and quantum levels. Remarkably, at the quantum level the negative norm states are eliminated, as well as the problems of unbounded below energy and non-unitary time evolution. We illustrate the idea of our approach by eliminating the negative norm states in a complex oscillator. Next, we extend the procedure to the Pais-Uhlenbeck oscillator. The corresponding quantum propagators are calculated using Schwinger's quantum action principle. We also discuss the equal frequency case at the classical level
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