Related papers: Mathematical renormalization in quantum electrodyn…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
A systematic formalism for quantum electrodynamics in a classical uniform magnetic field is discussed. The first order radiative correction to the ground state energy of an electron is calculated. This then leads to the anomalous magnetic…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…
The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
We present an extremely simple solution to the renormalization of quantum electrodynamics based on Epstein-Glaser approach to renormalization theory.
We extend the concept of the functional renormalization for quantum many-body problems to non-equilibrium situations. Using a suitable generating functional based on the Keldysh approach, we derive a system of coupled differential equations…
A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electromagnetic continuum within the framework of the functional renormalization group. The formalism allows us to determine complete physical…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…
We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start…
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
We study renormalization group flow in a non-local version of quantum electrodynamics (QED). We determine the regime in which the theory flows to a local theory in the infrared and study a possible UV completion of four-dimensional QED. In…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We discuss the ways of extracting a low energy scale of an underlying theory using high energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power…
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of…
$ $In this paper we present a systematic treatment for fundamental renormalization of quantum electrodynamics in real space. Although the standard renormalization is an old school problem in this case, it has not yet been completely done in…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…