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The theory of Quantum Mechanics requires \'completeness\', that is, we need to know the complete set of physically allowed states before we can reliably compute quantum mechanical amplitudes. Among these possible states are microscopic black holes, since they are valid solutions to Einstein\'s equations for the gravitational force. However, a quantum description of black holes requires a drastic revision of our notions of space and time, in particular if we were to accept the interpretation of their microstates as given by superstring theories. The logical foundations of our physical world view are touched upon here. A natural sounding solution of our problems here could come from a re-interpretation of what quantum mechanics really is. The first thing to dispose of should be all references to \'magic\' and \'mystery\' when dealing with quantum mechanics or string theory.

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.

At first sight, the ERG does not sit well with gauge theories: a naive implementation of the momentum cutoff central to the ERG breaks gauge invariance. However, things are not as they seem. Not only is it possible to construct a gauge invariant cutoff, but it is possible to construct manifestly gauge invariant ERGs. I will discuss the formulation, what has been achieved to date, and what can reasonably be hoped for in the future.

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.

Constructing good quantum LDPC codes remains an important problem in quantum coding theory. We contribute to the ongoing discussion on this topic by proposing two approaches to constructing quantum LDPC codes. In the first, we rely on an algebraic method that uses a redundant description of the parity check matrix to overcome the problem of 4-cycles in the Tanner graph that degrade the performance of iterative decoding. In the second we use the fact that subsystem coding can simplify the decoding process. We show that if there exist classical LDPC codes with large error exponents, then we can construct degenerate subsystem LDPC codes with the stabilizer generators having low weight.