Related papers: Fields topology and perturbation theory
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
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…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying…
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…
A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the BRST cohomology realizing the physical Hilbert space and the coboundary operator given by the calculations of tunneling…
A framework is proposed that allows to write down field theories with a new energy scale while explicitly preserving Lorentz invariance and without spoiling the features of standard quantum field theory which allow quick calculations of…
We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a…
The invariance of physical observables under redefinitions of the quantum fields is a well-known and important property of quantum field theory. We study perturbative field redefinitions in effective theories, paying special attention to…
General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics.…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
We investigate the effect on cosmological evolution of a strongly coupled quantum field that undergoes renormalization group flow from a UV CFT to an IR CFT. The field theory is defined by perturbation of a holographic CFT by a relevant…
The issue of field redefinition invariance of path integrals in quantum field theory is reexamined. A ``paradox'' is presented involving the reduction to an effective quantum-mechanical theory of a $(d+1)$-dimensional free scalar field in a…
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…
The spherical field formalism---a nonperturbative approach to quantum field theory---was recently introduced and applied to phi^4 theory in two dimensions. The spherical field method reduces a quantum field theory to a finite-dimensional…
Boundary quantum field theory is investigated in the Lagrangian framework. Models are defined perturbatively around the Neumann boundary condition. The analyticity properties of the Green functions are analyzed: Landau equations, Cutkosky…
In this review article, we discuss the current status and future prospects of perturbation theory as a means of studying the equilibrium thermodynamic and near-equilibrium transport properties of deconfined QCD matter. We begin with a brief…
A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This…