Related papers: BPHZ Renormalization in Configuration Space for th…
Arguments are provided which show that extension of renormalizability in quantum field theory is possible. A dressed scheme for the perturbation expansion is proposed. It is proven that in this scheme a nonrenormalizable interaction becomes…
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…
We introduce a two-dimensional, distribution-valued field which we call the quadratic field associated to the one-dimensional Ornstein-Uhlenbeck process. We show that the stationary quadratic fluctuations of the simple exclusion process,…
We present a systematic study of one-loop quantum corrections in scalar effective field theories from a geometric viewpoint, emphasizing the role of field-space curvature and its renormalisation. By treating the scalar fields as coordinates…
We build a toy model of the Wilson-Kogut renormalization group in one dimensional Quantum Mechanics. With it, we show how the RG flow in the space of 1-D S matrices of finite range defines, as renormalized interactions, the known four…
We consider scalar field theories in dimensions lower than four in the context of the Wegner-Houghton renormalization group equations (WHRG). The renormalized trajectory makes a non-perturbative interpolation between the ultraviolet and the…
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…
We provide a renormalization procedure for Phi-derivable approximations in theories coupling different types of fields. We illustrate our approach on a scalar phi^4 theory coupled to fermions via a Yukawa-like interaction. The…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
We consider the relativistic electron-positron field interacting with itself via the Coulomb potential defined with the physically motivated, positive, density-density quartic interaction. The more usual normal-ordered Hamiltonian differs…
The Kadanoff-Wilson-Fisher approach to renormalization is based upon studying the renormalization transform, which may be described as an action of the monoid $\mathbb{R}^{\times}_{\geq 1}$ on a suitable space of interactions. It is…
We study a first-order formulation for the coupled evolution of a quantum scalar field and a classical Friedmann universe. The model is defined by a state dependent hamiltonian constraint and the time dependent Schr\"odinger equation for…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form…
A Lagrange multiplier field restricts the quantum corrections to the Einstein-Hilbert action at one-loop order, yielding a model that is renormalizable and unitary while reproducing the Einstein field equations in the classical limit.
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…
Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate…
The biorthogonal formalism extends conventional quantum mechanics to the non-Hermitian realm. It has, however, been pointed out that the biorthogonal inner product changes with the scaling of the eigenvectors, an ambiguity whose physical…
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…
When a system is driven across a quantum critical point at a constant rate its evolution must become non-adiabatic as the relaxation time $\tau$ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging…