J. Julve

Ostrogradski formalism for higher derivative scalar field theories

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 higher-derivative gravity.

Time of arrival in the presence of interactions

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.

Higher-derivative boson field theories and constrained second-order theories

As an alternative to the covariant Ostrogradski method, we show that higher-derivative (HD) relativistic Lagrangian field theories can be reduced to second differential order by writing them directly as covariant two-derivative theories involving Lagrange multipliers and new fields. Despite the intrinsic non-covariance of the Dirac procedure used to deal with the constraints, the explicit Lorentz invariance is recovered at the end. We develop this new setting on the basis of a simple scalar model and then its applications to generalized electrodynamics and HD gravity are worked out. For a wide class of field theories this method is better suited than Ostrogradskis for a generalization to 2n-derivative theories.

Nonlinear group realizations and Higgs-like mechanism

SummaryAn approach to the concept of nonlinear realizations of group symmetries is considered. Some physically interesting applications are suggested. In particular, a method to give masses to the gauge mesons without (even spontaneously) breaking the symmetry is proposed.RiassuntoSi considera un approccio al concetto di realizzazioni non lineari di simmetrie di gruppo. Alcune applicazioni fisicamente interessanti sono suggerite. In particolare, si propone un metodo per dare masse ai mesoni di gauge senza (anche spontaneamente) violare la simmetria.РезюмеРассматривается подход к концепции нелинейных реализаций групп симметрии. Обсуждаются некоторые физически интересные приложения. В частности, предлагается метод получения масс калибровочных мезовон без нарушения симметрии (даже спонтанно).

Tunnelling of plane waves through a square barrier

The time evolution of plane waves in the presence of a one-dimensional square quantum barrier is considered. Comparison is made between the cases of an infinite and a cut-off (shutter) initial plane wave. The difference is relevant when the results are applied to the analysis of the tunnelling regime. This work is focused on the analytical calculation of the time-evolved solution and highlights the contribution of the resonant (Gamow) states.

An alternative way to the direct product of groups

SummaryWe propose a mechanism that describes an alternative procedure to the direct product of groups by involving some scalar fields related to the group parameters. In particular, the method may provide a framework for grand unified theories with a minimal increase in the number of fundamental fields required.RiassuntoSi propone un meccanismo che descrive una procedura alternativa al prodotto diretto di gruppi coinvolgendo campi scalari correlati ai parametri di gruppi. In particolare, il metodo può fornire una base alla teoria della grande unificazione con un incremento minimo del numero di campi fondamentali richiesto.РезюмеМы предлагаем механизм, который описывает альтернативную процедуру получения прямого произведения групп, посредством включения некоторых скалярных полей, связанных с параметрами груии. В частности, предложенный метод может обеспечить основу для великой единой теории с минимальным увеличением числа требуемых фундаментальных полей.