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Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
Field theories are usually quantized by performing a path integral over configurations of classical fields. This is the case both in perturbation theory and in Wilson's nonperturbative lattice field theory. D-theory is an alternative…
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
This paper is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first section we give proposal for axioms for a euclidean field theory on a sphere in terms of C*-algebras. Then, in the second…
We give a new representation of Euclidean quantum fields as scaling limits of systems of interacting, continuous, classical particles in the grand canonical ensemble.
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4 model. The regularisation consists of a fuzzy sphere with radius R for the two…
We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to…
The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three…
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical…
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
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…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…