相关论文: Quantization of three-wave equations

We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…

The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…

We develop the approach to the problem of integrable discretization based on the notion of $r$--matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems with the Lax matrices of the underlying…

In this paper we present and test a full discretization of all elements of the Calder\'on Calculus (layer potentials and integral operators) for the Helmholtz equation in smooth closed curves in the plane. The resulting integral equations…

We consider three common mathematical models for time-harmonic high frequency scattering: the Helmholtz equation in two and three spatial dimensions, a transverse magnetic problem in two dimensions, and Maxwell's equation in three…

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…

Both unitary evolution and the effects of dissipation and decoherence for a general three-level system are of widespread interest in quantum optics, molecular physics, and elsewhere. A previous paper presented a technique for solving the…

Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity''…

The formalism relating the relativistic three-particle infinite-volume scattering amplitude to the finite-volume spectrum has been developed thus far only for identical or degenerate particles. We provide the generalization to the case of…

The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…

The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…

A dynamical scheme of quantization of symplectic manifolds is described. It is based on intrinsic Schr\"odinger and Heisenberg type nonlinear evolutionary equations with multidimensional time running over the manifold. This is the…

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are…

With advances in quantum computing, new opportunities arise to tackle challenging calculations in quantum field theory. We show that trotterized time-evolution operators can be related by analytic continuation to the Euclidean transfer…

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…

For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or…

In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…