Related papers: Curiosities on Free Fock Spaces
Future neutrino and cosmological experiments will perform powerful searches for new light particles. After a general introduction we discuss how a new light fermion (`sterile neutrino') could manifest.
Novel controlled non-perturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
We study the quantization of a linear scalar field, whose symmetries are described by the kappa-Poincare' Hopf-algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (planckian) cut-off for…
In this paper we provide a novel and general way to construct the result of the action of any bosonic or fermionic operator represented in second quantized form on a state vector, without resorting to the matrix representation of operators…
Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…
This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…
These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.
We solve the time evolution of the density matrix both for fermions and bosons in the presence of a homogeneous but time dependent external electric field. The number of particles produced by the external field, as well as their…
Fermion-boson stars are solutions of the gravitationally coupled Einstein-Klein-Gordon-Hydrodynamic equations system. By means of methods developed in previous works, we perform a stability analysis of fermion-boson stars that include a…
The factorizable vectors of a complete Boolean algebra of type I factors, acting on a separable Hilbert space, are shown to be total, resolving a conjecture of Araki and Woods. En route, the spectral theory of noise-type Boolean algebras of…
The road towards unification of elementary interactions is thought to start on the solid ground of a universal local gauge principle. I discuss the different types of bosonic gauge symmetries in gravitational and nongravitational (standard…
We use the light front ``machinery'' to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front…
The phenomenon of Bose-like condensation, the continuous change of the dimensionality of the particle distribution as a consequence of freezing out of one or more degrees of freedom in the low particle density limit, is investigated…
As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…
Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level…
We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth non-singular Fermi liquid interactions we obtain Shankar's renormalization- group flows and reproduce…
It is shown that the classical field equations pertaining to gravity coupled to other bosonic fields are equivalent to a single geodesic equation, describing the free fall of a point particle in superspace. Some implications for quantum…
These lectures are an introduction to the physics of strongly correlated fermions and bosons. They are specially targeted for the experimental realizations that have been provided by cold atomic gases in optical lattices.
We have developed a quantum field theoretic framework for scalar and pseudoscalar meson mixing and oscillations in time. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is proven…