Related papers: Quantum Fields and Probability
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
A simple introduction of renormalization in quantum field theory is discussed. Explanation of concepts is emphasized instead of the technical details.
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for…
A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…
These lectures review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective…
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative GFT (spin foam)…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
We motivate the possibility of using notions and methods derived from quantum physics, and more specifically from the research field known as 'quantum cognition', to optimally model different situations in the field of medicine, its…
Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…
We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field…
In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
The renormalization group has played an important role in the physics of the second half of the twentieth century both as a conceptual and a calculational tool. In particular it provided the key ideas for the construction of a qualitative…