Related papers: Hilbert space formalisms for group field theory
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of…
We summarize the main ideas behind TGFT condensate cosmology and sketch the technical steps that bring from the fundamental theory to the effective cosmological dynamics. This framework is presented as an explicit illustration of (and…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
For a quantum field living on a non - static spacetime no instantaneous Hamiltonian is definable, for this generically necessitates a choice of inequivalent representation of the canonical commutation relations at each instant of time. This…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a…
In this review we focus on the main cosmological implications of the Group Field Theory approach, according to which an effective continuum macroscopic dynamics can be extracted from the underlying formalism for quantum gravity. Within this…
We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…
We present a new Group Field Theory for 4d quantum gravity. It incorporates the constraints that give gravity from BF theory, and has quantum amplitudes with the explicit form of simplicial path integrals for 1st order gravity. The…