Astrophysics

Recent developments in the field of Numerical Relativity have not only provided key insights of binary black hole systems but also began influencing its future role. Undoubtedly one of the most important future drivers in the near future of the field will be its role as another element within the study of spectacular astrophysical phenomena involving strongly gravitation scenarios. Connecting (yet to be observed) gravitational waves with observations within the electromagnetic spectra will be one ultimate goal of this enterprise. This talk will illustrate this interplay within the study of magnetized binary neutron star systems as a stepping stone towards more ambitious goals.

I will review relativistic quantum theory that is based on Wigner\'s unitary representations of the Poincare group, Dirac\'s forms of dynamics, and Newton-Wigner\'s definition of the position operator. Formulas will be derived that transform particle observables between different inertial reference frames. In the absence of interactions, these formulas coincide with Lorentz transformations from special relativity. However, when interaction is turned on, some deviations appear. The relationship of this result to the Currie-Jordan-Sudarshan \'no-interaction\' theorem will be mentioned, and the status of Lorentz transformations within quantum and classical theories of interacting particles will be discussed.

Wigner-Dirac relativistic quantum theory is applied to decay laws of an unstable particle in different reference frames. It is shown that decay slows down from the point of view of the moving observer, as expected. However, small deviations from Einstein\'s time dilation formula are also found. The origin of these deviations is discussed, as well as possibilities for their experimental detection.

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

I will review an old (Greenberg and Schweber, 1958) and undeservedly forgotten idea in quantum field theory. This idea allows one to reformulate QFT as a Hamiltonian theory of physical (rather than bare) particles and their direct interactions. The dressed particle approach is scattering-equivalent to the traditional one, however it doesn\'t require renormalization and may provide a valuable tool for calculations of wave functions of bound states and time evolution.

The Hamiltonian of traditionally adopted detector models features out of diagonal elements between the vacuum and the one particle states of the field to be detected. We argue that reasonably good detectors, when written in terms of fundamental fields, have a more trivial response on the vacuum. In particular, the model configuration ``detector in its ground state + vacuum of the field\' generally corresponds to a stable bound state of the underlying theory (e.g. the hydrogen atom in a suitable QED with electrons and protons) and therefore should be also an eigenstate of the model Hamiltonian. As a concrete example, we study a consistent ``fundamental\' toy field theory where a stable particle can capture a light quantum and form a quasi-stable state. To such stable particle correspond eigenstates of the full theory, as is shown explicitly by using a dressed particle formalism at first order in perturbation theory. We then write the corresponding Hamiltonian for a model detector (at rest) where the stable particle and the quasi-stable configurations correspond to the two internal levels, ``ground\' and ``excited\', of the detector. The accelerated version of this Hamiltonian is inevitably model dependent emph{i.e.} it will generally depend on how the stable particle/detector is forced along the accelerated trajectory. However, in its most basic version, the accelerated detector doesn\'t see Unruh radiation.

Many string theorists and cosmologists have recently turned their attention to building and testing string theory models of inflation. One of the main goals is to find novel features that could distinguish stringy models from their field theoretic counterparts. This is difficult because, in most examples, string theory is used to derived an effective theory operating at energies well below the string scale. However, since string theory provides a complete description of dynamics also at higher energies, it may be interesting to construct inflationary models which take advantage of this distinctive feature. I will discuss recent progress in this direction using p-adic string theory - a toy model of the bosonic string for which the full series of higher dimensional operators is known explicitly - as a playground for studying string cosmology to all order in $alpha\'$. The p-adic string is a nonlocal theory containing derivatives of all orders and this structure is also ubiquitous in string field theory. After discussing the difficulties (such as ghosts and classical instabilities) that arise in working with higher derivative theories I will show how to construct generic inflationary models with infinitely many derivatives. Novel features include the possibility of realizing slow roll inflation with a steep potential and large nongaussian signatures in the CMB.

We introduce a formalism allowing us to localize a certain class of theories with an infinite number of derivatives (nonlocal), which include effective actions of string field theory. The number of degrees of freedom is finite and the Cauchy problem, Hamiltonian and quantization are all well-defined. As applications, the rolling tachyon of cubic string field theory and some cosmological toy models are considered.

Hawking\'s black hole information paradox is one of the great thought experiments in physics. It points to a breakdown of some central principle of physics, though which one breaks down is still in dispute. It has led to the discovery of ideas that seem to be key to unifying quantum mechanics and gravity, namely the holographic principle and gauge/gravity duality. I review this subject, and discuss ongoing work and future directions.