Related papers: Quantum Field Theory of Classically Unstable Hamil…
A soluble model for the relativistically description of an unstable system is given in terms of relativistic quantum field theory, with a structure similar to Van Hove's generalization of the Lee model in the non-relativistic theory.
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
Classical gravity coupled to a CFT$_4$ (matter) is considered. The effect of the quantum dynamics of matter on gravity is studied around maximally symmetric spaces (flat, de Sitter and Anti de Sitter). The structure of the graviton…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Quasi-periodically driven quantum parametric oscillators have been the subject of several recent investigations. Here we show that for such oscillators, the instability zones of the mean position and variance (alternatively the mean energy)…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
After reviewing the covariant description of Hamiltonian dynamics, some applications are done to the non-relativistic isotropic three-dimensional harmonic oscillator, Rovelli's model, and SO(3,1) BF theories.
We develop a novel framework for describing quantum fluctuations in field theory, with a focus on cosmological applications. Our method uniquely circumvents the use of operator/Hilbert-space formalism, instead relying on a systematic…
A system of chromodynamic fields, which can be treated as classical, is generated at the earliest stage of relativistic heavy-ion collisions. Numerical simulations show that the system is unstable but the nature of the instability is not…