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Register a new userEffective constrained polymeric theories and their continuum limit
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The classical limit of polymer quantum theories yields a one parameter family of `effective theories labeled by lambda. Here we consider such families for constrained theories and pose the problem of taking the `continuum limit, lambda -> 0. We put forward criteria for such question to be well posed, and propose a concrete strategy based in the definition of appropriately constructed Dirac observables. We analyze two models in detail, namely a constrained oscillator and a cosmological model arising from loop quantum cosmology. For both these models we show that the program can indeed be completed, provided one makes a particular choice of lambda-dependent internal time with respect to which the dynamics is described and compared. We show that the limiting theories exist and discuss the corresponding limit. These results might shed some light in the problem of defining a renormalization group approach, and its associated continuum limit, for quantum constrained systems.
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Effective theory of fluctuations based on underlying symmetry plays very important role in understanding the low energy phenomena. Using this powerful technique we study the fluctuation dynamics keeping in mind the following central question: does the effective theory of black hole provide any information about the possible existence of hair? Assuming the symmetry of the hair being that of the underlying black hole space-time, we start by writing down the most general action for the background and the fluctuation in the effective field theory framework. Considering the asymptotically flat and de Sitter black hole background with a spherically symmetric hair we derived the most general equation of motion for the fluctuation. For a particular choice of theory parameters, quasinormal modes corresponding to those fluctuations appeared to have distinct features compared to that of the usual black hole quasinormal modes. The background equations from the effective theory Lagrangian, on the other hand, seemed to suggest that the underlying theory of the hair under consideration should be higher derivative in nature. Therefore as a concrete example we construct a class of higher derivative scalar field theory which gives rise to spherically symmetric hair through background cosmological constant. We also calculate the quasinormal modes whose behaviour turned out to be similar to the one discussed from the effective theory.
We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.
The Lorentzian distance formula, conjectured several years ago by Parfionov and Zapatrin, has been recently proved by the second author. In this work we focus on the derivation of an equivalent expression in terms of the geometry of 2-spinors by using a partly original approach due to the first author. Our calculations clearly show the independence of the algebraic distance formula of the observer.
We consider a five-dimensional Einstein--Cartan spacetime upon which Dirac spinor fields can be defined. Dirac spinor fields in five and four dimensions share many features, like the fact that both are described by four-component spinor fields, but they are also characterized by strong differences, like the fact that in five dimensions we do not have the possibility to project on left-handed and right-handed chiral parts unlike what happens in the four-dimensional instance: we conduct a polar decomposition of the spinorial fields, so to highlight all similarities and discrepancies. As an application of spinor fields in five dimensions, we study Bianchi-I spacetimes, verifying whether the Dirac fields in five dimensions can give rise to inflation or dark-energy dominated cosmological eras or not.
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. I
n particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
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