Related papers: Fields topology and perturbation theory
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
A scalar field theory is constructed on an energy-momentum background of constant curvature. The generalization of the usual Feynamn rules for the flat geometry follows from the requirement of their covariance. The main result is that the…
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…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
The perturbation theory over inverse interaction constant $1/g$ is constructed for Yang-Mills theory. It is shown that the new perturbation theory is free from the gauge ghosts and Gribov's ambiguities, each order over $1/g$ presents the…
A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
In this paper we will analyse some interesting structures that occur in scalar quantum field theory. We will quantize this theory using path integrals. We will analyse the Bogomolny Bound for scalar quantum field theory in two dimensions.…
The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…
Many proposals have been put forth for controlling quantum phenomena, including open-loop, adaptive feedback, and real-time feedback control. Each of these approaches has been viewed as operationally, and even physically, distinct from the…
These two lectures give a pedagogical introduction to the ``string-inspired'' worldline technique for perturbative calculations in quantum field theory. This includes an overview over the present range of its applications. Several examples…
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces.…
Motivated by the recent interest in the criticality of open quantum many-body systems, we study nonlinear sigma models with complexified couplings as a general framework for nonunitary field theory. Applying the perturbative…