Related papers: Elliptically Oscillating Classical Solution in Hig…
The elliptically oscillating solutions in the Abelian Higgs-model are presented and the classical massive-dispersion-relation through the non-linear dynamics is discussed. The generated massive-dispersion-relation including a field value of…
A particular solution to the equations of motion of the Abelian Higgs model is given. The solution involves the Jacobi elliptic functions as well as the Heun functions.
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…
We discuss the dynamics of the quantum fluctuation around the nonlinear massive wave solution in the Higgs potential. In particular, we analyze the stability and instability of the mode function. Using the stability condition for Hill's…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
Motivated by cosmological examples we study quantum field theoretical tunnelling from an initial state where the "classical field", i.e. the vacuum expectation value of the field operator is spatially homogeneous but performing a…
Alternative forms of the solutions to the quantum field equations and their implications for physical theory are considered. Incorporation of these alternative solution forms, herein deemed "supplemental solutions", into the development of…
We consider two one dimensional nonlinear oscillators, namely (i) Higgs oscillator and (ii) a $k$-dependent nonpolynomial rational potential, where $k$ is the constant curvature of a Riemannian manifold. Both the systems are of position…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
We study a class of oscillating bounce solutions to the Euclidean field equations for gravity coupled to a scalar field theory with two, possibly degenerate, vacua. In these solutions the scalar field crosses the top of the potential…
The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
The prospect of a time-dependent Higgs vacuum expectation value is examined within the standard model of electroweak interactions. It is shown that the classical equation of motion for the Higgs field admits a solution that is a…
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann…
I describe a class of oscillating bounce solutions to the Euclidean field equations for gravity coupled to a scalar field theory with multiple vacua. I discuss their implications for vacuum tunneling transitions and for elucidating the…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact…