Related papers: Renormalization and Computation II: Time Cut-off a…
We study global quenches in a number of interacting quantum field theory models away from the conformal regime. We conduct a perturbative renormalization at one-loop level and track the modifications of the quench protocol induced by the…
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger…
This is a conceptual paper that re-examines the principles underlying the application of renormalization theory to quantum phase transitions in the light of quantum information theory. We start by describing the intuitive argument known as…
In the Hopf algebra approach of Connes and Kreimer on renormalization of quantum field theory, the renormalization process is views as a special case of the Algebraic Birkhoff Decomposition. We give a differential algebra variation of this…
A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are…
The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…
We study renormalization in a kinetic scheme using the Hopf algebraic framework, first summarizing and recovering known results in this setting. Then we give a direct combinatorial description of renormalized amplitudes in terms of Mellin…
Central in the Hopf algebra approach to the renormalization of perturbative quantum field theory of Connes and Kreimer is their Algebraic Birkhoff Decomposition. In this tutorial article, we introduce their decomposition and prove it by the…
Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. Quantum computers are suggested as one route to propagating quantum systems far more efficiently than ordinary numerical…
A quenched second order phase transition is modeled by an effective $\Phi^4$-theory with a time-dependent Hamiltonian $\hat{H} (t)$, whose symmetry is broken spontaneously in time. The quantum field evolves out of equilibrium…
We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative…
We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states,…