Related papers: KAM Theorem and Quantum Field Theory
A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for…
A new formalism is given for the renormalization of quantum field theories to all orders of perturbation theory, in which there are manifestly no overlapping divergences. We prove the BPH theorem in this formalism, and show how the local…
In this paper, we establish a KAM-theorem for ordinary differential equations with finitely differentiable vector fields and multiple degeneracies. The theorem can be used to deal with the persistence of quasi-periodic invariant tori in…
We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises…
We develop quantum-optical input-output theory for resonators with arbitrary coupling strength, and for input fields whose spectrum can be wider than the cavity free-spectral range, while ensuring that the field-operator commutator…
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and…
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…
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…
We reexamine a unitary-transformation method of extracting a physical Hamiltonian from a gauge field theory after quantizing all degrees of freedom including redundant variables. We show that this {\it quantum Hamiltonian reduction} method…
We derive quantum field theory Ward identities based on linear area preserving and conformal transformations in 2+1 dimensions. The identities relate Hall viscosities, Hall conductivities and the angular momentum. They apply both for…
We prove that there is an invariant torus with given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for…
The theory of quantum fields propagating on an isotropic cosmological quantum spacetime is reexamined by generalizing the scalar test field to an electromagnetic (EM) vector field. For any given polarization of the EM field on the classical…
In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann. In our formalism the entries of the retarded products…
In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalisation Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus…
In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy…
The goal of this paper is to develop a KAM theory for tori with hyperbolic directions, which applies to Hamiltonian partial differential equations, even to some ill-posed ones. The main result has an \emph{a-posteriori} format, i.e., we…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
~It is shown that the quantum massive non-Abelian field theory established in the former papers is renormalizable. This conclusion is achieved with the aid of the Ward-Takahashi identities satisfied by the generating functionals which were…
In this paper, we investigate the existence of KAM tori for an infinite dimensional Hamiltonian system with finite number of zero normal frequencies. By constructing a constant quantity we show that, for "most" frequencies in the sense of…
The effect of Kolmogorov-Arnold-Moser (KAM) theorem in quantum systems is manifested in dividing eigenstates into regular and irregular states. We propose an effective method based on Wannier basis in phase space to illustrate this division…