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We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
There are many possible gravitational applications of an effective approach to Quantum Field Theory (QFT) in curved space. We present a brief review of effective approach and discuss its impact for such relevant issues as the cosmological…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
This is a review of some of the concepts and results of the effective field theory treatment of quantum general relativity. Included are lessons of low energy quantum gravity, and a discussion of the limits of effective field theory…
We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…
This essay intends to present a novel approach to the concept of "transaction" in quantum physics. Breaking with Cramer's original theory, the transaction is not connected to the simultaneously retarded and advanced spacetime propagation of…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
General relativity is applied to the strong interaction; the nexus between the two being arrived at by constructing a line element having the Yukawa form, which is used to describe geometrically the classical dynamics of a particle moving…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
It is shown that adopting the \emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can…