We carry out the extension of the Ostrogradski method to relativistic field theories. Higher-derivative Lagrangians reduce to second differential-order with one explicit independent field for each degree of freedom. We consider a higher-derivative relativistic theory of a scalar field and validate a powerful order-reducing covariant procedure by a rigorous phase-space analysis. The physical and ghost fields appear explicitly. Our results strongly support the formal covariant methods used in higherderivative gravity.
We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the interacting cases to compute t in the context of the positive-operator-valued measures. We then compute the probability distribution in the times of arrival at a point for particles that have undergone reflection, transmission or tunneling off finite potential barriers. For narrow Gaussian initial wave packets we obtain multimodal time distribution of the reflected packets and a combination of the Hartman effect with unexpected retardation in tunneling. We also employ explicitly our formalism to deal with arrivals in the interaction region for the step and linear potentials.
The flower derivative) action, which describes the actual degrees of freedom of a (higher derivative) lheoly of gravity quadratic in the scalar and Ricci curvatures, is found. Key steps are a Legendre transform and a suitable diagonalidon procedure. Some consequences of this insight are outlined.
We present a general scheme for the nonlinear gauge realizations of spacetime groups on coset spaces of the groups considered. In order to show the relevance of the method for the rigorous treatment of the translations in gravitational gauge theories, we apply it in particular to the a ne group. This is an illustration of the family of spacetime symmetries having the form of a semidirect product H T, where H is the stability subgroup and T are the translations. The translational component of the connection behaves like a true tensor under H when coset realizations are involved.
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