Related papers: On the trees of quantum fields

One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…

By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…

This paper is a brief mathematical excursion which starts from quantum electrodynamics and leads to the Moebius function of the Tamari lattice of planar binary trees, within the framework of groups of tree-expanded series. First we recall…

An explicit perturbative solution to all orders is given for a general class of nonlinear differential equations. This solution is written as a sum indexed by rooted trees and uses the Green function of a linearization of the equations. The…

A one-dimensional quantum wire of Fermions is considered and ground state properties are calculated in the high density regime within the extended quasiparticle picture and Born approximation. Expanding the two-particle Green functions…

A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…

A new version of application Pauli-Villars regularized Green functions in the quantum field theory using higher derivatives is proposed. In this version the regularizing mass $M$ is large but finite. Our approach is demonstrated and…

We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision…

To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting…

The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these…

Using electromagnetic interaction as an example, response transformations [L.P. and S.S., Ann.Phys. 323, 1963, 1989 (2008), 324, 600 (2009)] are applied to the standard perturbative approach of quantum field theory. This approach is…

A derivation is given of the Feynman rules to be used in the perturbative computation of the Green's functions of a generic quantum many-body theory when the action which is being perturbed is not necessarily quadratic. Some applications…

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be…

A quantum-field approach for describing many-particle Fermi systems at finite temperatures and with spontaneously broken symmetry has been proposed. A generalized model of self-consistent field (SCF), which allows one to describe the states…

Field transformations for the quantum effective action lead to different pictures of a given physical situation, as describing a given evolution of the universe by different geometries. Field transformations for functional flow equations…

A transport theory which is not restricted to the gradient and quasi-particle approximations is presented which is formulated in terms of the energy moments, or equivalently the equal-time derivatives of the one-particle Green functions. A…

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…

We analyse nonperturbatively signal transmission patterns in Green's functions of interacting quantum fields. Quantum field theory is re-formulated in terms of the nonlinear quantum-statistical response of the field. This formulation…

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…