Alternative Symmetries in Quantum Field Theory and Gravity

A general, incomplete and partisan overview of various areas of the theoretical investigation is presented. Most of this activity stems from the search for physics beyond quantum field theory and general relativity, a titanic struggle that, in my opinion, empowered the symmetry principles to a dangerous level of speculation. In the works (that are my own) commented upon here the attempt has been to proceed by holding to certain epistemological pillars (usually absent from the too speculative theories) such as, e.g., four or less dimensions, proposals for experimental tests of radical ideas, wide cross-fertilization, etc.. As for the latter, the enterprise is undertaken within a theoretical perspective that pushes till condensed matter and even biology the cross-fertilization between ``branches of physics''.Comment: 42 pages, 1 figure, Habilitation (associate professorship) dissertation at Charles University in Prague, the papers of Section 5 are not included but easy to fin

Graphene and Black Holes: novel materials to reach the unreachable

The case for a dedicated laboratory, to test hep-th models on analogue systems, is briefly made. The focus is on graphene.Comment: 3 pages; invited to talk to the workshop "New Frontiers in Multiscale Modelling of Advanced Materials", ECT*, Trento, June 17-20, 2014; to appear in Frontiers in Material

Revisiting the gauge fields of strained graphene

We show that, when graphene is only subject to strain, the spin connection gauge field that arises plays no measurable role, but when intrinsic curvature is present and strain is small, spin connection dictates most the physics. We do so by showing that the Weyl field associated with strain is a pure gauge field and no constraint on the $(2+1)$-dimensional spacetime appears. On the other hand, for constant intrinsic curvature that also gives a pure-gauge Weyl field, we find a classical manifestation of a quantum Weyl anomaly, descending from a constrained spacetime. We are in the position to do this because we find the equations that the conformal factor in $(2+1)$-dimensions has to satisfy, that is a nontrivial generalization to $(2+1)$-dimensions of the classic Liouville equation of differential geometry of surfaces. Finally, we comment on the peculiarities of the only gauge field that can describe strain, that is the well known {\it pseudogauge field} $A_1 \sim u_{11} - u_{22}$ and $A_2 \sim u_{12}$, and conclude by offering some scenarios of fundamental physics that this peculiar field could help to realize.Comment: 24 pages, 6 figures. Comments added, text reduced and relevant references include

QUANTUM DISSIPATION AND QUANTUM GROUPS

We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov transformations in terms of operators of the quantum Weyl-Heisenberg algebra. The quantum parameter acts as a label for the unitarily inequivalent representations of the canonical commutation relations in which the space of the states splits in the infinite volume limit.Comment: to appear in Annals of Physics (N.Y.