Related papers: Quantum Theory and Galois Fields
I give a very brief introduction to the use of effective field theory techniques in quantum calculations of general relativity. The gravitational interaction is naturally organized as a quantum effective field theory and a certain class of…
We present a new approximation technique for quantum field theory. The standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In a…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
Quantum field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
As shown in our publications, quantum theory based on a finite ring of characteristic $p$ (FQT) is more general than standard quantum theory (SQT) because the latter is a degenerate case of the former in the formal limit $p\to\infty$. One…
We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality.…
The incompatibility between GR and QM is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - QM gives a universally valid basis for the description of all natural…
I provide a conceptually-focused presentation of `low-energy quantum gravity' (LEQG), the effective quantum field theory obtained from general relativity and which provides a well-defined theory of quantum gravity at energies well below the…
One of the fundamental challenges for quantum cosmology is to explain the emergence of our macroscopic Universe from physics at the Planck scale. In the group field theory (GFT) approach to quantum gravity, such a macroscopic universe…
We provide a short and non-technical summary of our current knowledge and some possible perspectives on the group field theory formalism for quantum gravity, in the form of a (partial) FAQ (with answers). Some of the questions and answers…
Understanding the quantum nature of spacetime and gravity remains one of the most ambitious goals of theoretical physics. It promises to provide key new insights into fundamental particle theory, astrophysics, cosmology and the foundations…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…
Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is…
To date, both quantum theory, and Einstein's theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be…