Related papers: Mathematical renormalization in quantum electrodyn…
It is shown how to construct renormalization group flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation…
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…
Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical…
Wilson's Numerical Renormalization Group (NRG) is so far the only nonperturbative technique that can reliably access low-energy properties of quantum impurity systems. We present a recent extension of the method, the DM-NRG, which yields…
The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The…
We review two different noncommutative gauge models generalizing approaches which lead to renormalizable scalar quantum field theories. One of them implements the crucial IR damping of the gauge field propagator in the so-called ``soft…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
In several preceding studies, the explicitly covariant formulation of light front dynamics was developed and applied to many observables. In the present study we show how in this approach the renormalization procedure for the first…
Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
In this study, we delve into the intricate mathematical frameworks essential for the renormalization of effective elastic models within complex physical systems. By integrating advanced tools such as Laurent series, residue theorem, winding…
The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account,…
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We formulate a non-relativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and…
In all nontrivial cases renormalization, as it is usually formulated, is not a change of integration variables in the functional integral, plus parameter redefinitions, but a set of replacements, of actions and/or field variables and…
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))^2 and the…