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A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model…
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The…
An introduction to methods of effective field theory is given. Examples are presented, including Rayleigh scattering from nonrelativistic quantum mechnics, chiral perturbation theory/QCD as well as electromagnetic and weak interactions of…
We discuss a new simple field theory approach of Coulomb systems. Using a description in terms of fields, we introduce in a new way the statistical degrees of freedom in relation with the quantum mechanics. We show on a series of examples…
We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
This work starts from the premise that sinusoidal plane waves cease to be solutions of field theories when turning on an interaction. A nonlinear interaction term generates harmonics analogous to those observed in nonlinear optical media.…
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…
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is $2\pi$. A…
Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical…
A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic…
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…
Heavy quarkonium hybrids are studied in an effective field theory framework. Coupled and uncoupled Schr\"odinger equations are obtained for different quantum numbers of the hybrid states. The results are discussed and compared to other…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to…
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new type of interaction which depends on the relative velocity…