Related papers: Crossing singularities in the saddle point approxi…
The possibility of extending the canonical formulation of quantum mechanics (QM) to a space-time symmetric form has recently attracted wide interest. In this context, a recent proposal has shown that a spacetime symmetric many-body…
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…
Central to the power of quantum computing is the concept of quantum parallelism: quantum systems can explore and process multiple computational paths simultaneously. In this paper, we discuss the elusive nature of quantum parallelism,…
We describe in detail a physical situation in which instantons are necessarily complex, not just Wick rotations of classical solutions to Euclidean spacetime. These complex instantons arise in the semiclassical evaluation of vacuum pair…
In this work, we propose a dangerous journey -- a journey through the strong singularity from one universe to another or from inside of a black hole to its 'inverse' as a white hole. Such singularities are hidden in the Friedman and…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Quantum tunnelling phenomenon allows a particle in Schr\"odinger mechanics tunnels through a barrier that it classically could not overcome. Even the infinite potentials do not always form impenetrable barriers. We discuss an answer to the…
All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a…
This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes…
This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also…
Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more…
The paper contains description of the path integrals in the action-angle phase space. It allows to split the action and angle degrees of freedom and to show that the angular quantum corrections cancel each other if the classical classical…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…
Semiclassical methods are extremely important in the subjects of wave packet and coherent state dynamics. Unfortunately, these essentially saddle point approximations are considered nearly impossible to carry out in detail for systems with…
The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046, gr-qc/9704033]. The aim of the paper is to incorporate singularities---both local (black hole and naked singularity) and…
A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…