Related papers: Field Theory as a Matrix Model
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
The quantization of noncommutative scalar field theory is studied from the matrix model point of view, exhibiting the significance of the eigenvalue distribution. This provides a new framework to study renormalization, and predicts a phase…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
We discuss the algebra of $N\times N$ matrices as a reduced quantum plane. A $3-$nilpotent deformed differential calculus involving a complex parameter $q$ is constructed. The two cases, $q$ $3^{rd}$ and $N^{th}$ root of unity are…
In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and chi^2phi theories are considered. The motivation behind the applications discussed in…
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
It is well-known that non-commutative (NC) field theories at theta = infinity are ``equivalent'' to large N matrix field theories to all orders in perturbation theory, due to the dominance of planar diagrams. By formulating a NC field…
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for…
We formulate minimal SuperGeometric Quantum Field Theories (SG-QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. First, we discuss the issue of uniqueness in defining the…
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…
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…
The motivations of the 1/N expansion method in quantum field theory are explained. The method is first illustrated with the O(N) model of scalar fields. A second example is considered with the two-dimensional Gross-Neveu model of fermion…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an…
A simple lattice model inducing a gauge theory is considered. The model describes an interaction of a gauge field to an $N\times N$ complex matrix scalar field transforming as a field in the fundamental representation. In contrast to the…
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in…
The light-front Hamiltonian formulation for the scalar field theory contains a new ingredient in the form of a constraint equation. Renormalization of the two dimensional $\phi^{4}$ theory, described in the continuum, is discussed. The mass…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
We present a complex field formulation of the quantum estimation theory that works natively with complex statistics on the dependence of complex parameters. This formulation states new complex versions of the main quantities and results of…