Related papers: Fermions in Loop Quantum Gravity and Resolution of…
We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality $S/\hbar\longleftrightarrow\hbar/S$, where S is the classical action, is equivalent to noncommutativity (of the Heisenberg-algebra type) of the…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore…
One of the principal aspects through which the effects of quantum gravity are hoped to manifest is the possible modification of the dispersion relation for electromagnetic (e-m) waves. By combining (i) the symmetry reduced approaches to…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of Yang-Mills gauge theories without making…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
Wilson fermion (WF) is a fundamental particle in the theory of quantum chromodynamics, originally proposed by Kenneth Wilson to solve the fermion doubling problem, i.e., more fermions than expected when one puts fermionic fields on a…
Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple…
We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic QFTs, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map…
A discussion of relativistic quantum-geometric mechanics on phase space and its generalisation to the propagation of free, massive, quantum-geometric scalar fields on curved spacetimes is given. It is shown that in an arbitrary coordinate…
In a quantum theory of gravity the gravitational Wilson loop, defined as a suitable quantum average of a parallel transport operator around a large near-planar loop, provides important information about the large-scale curvature properties…
The one- and the two-particle propagators for an infinite non-interacting Fermi system are studied as functions of space-time coordinates. Their behaviour at the origin and in the asymptotic region is discussed, as is their scaling in the…
Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
We revisit the phenomenon of the resonant transmission of fermionic carriers through a quantum device connected to two contacts with different chemical potentials. We show that, besides the traditional in solid-state physics…
We present a formalism for the fermionic quasiparticle propagator in a superfluid fermionic system. Starting from a general many-body hamiltonian confined by the two-body instantaneous interaction, the equation of motion for the fermionic…
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…