quantum theory poses itself to be a challenging counterpart to the intelligent design argument. quantum physics founded upon uncertainty, probability and statistics has exerted great influence since its inception on the philosophical thinking of man. the findings of this theory has helped bring about a dramatic transformation in the notion of ‘order in nature.’ in modern physics, it is hardly p...

While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating the ability to de-quantise quantum algorithms into classical simulations of the algorithms which are as efficient in both time and space as the original quant...

This is the fourth paper in a series of four which we use space adiabatic methods order to incorporate backreactions among homogeneous and between inhomogeneous degrees freedom quantum cosmological perturbation theory. In this paper, finally consider gauge invariant scalar (Mukhanov-Sasaki) tensor (primordial gravitational wave) perturbations General Relativity coupled an inflaton field arise f...

Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum m...

Quantum field theory (QFT) is the theory of elementary particles and their fundamental interactions. The very successful standard model which describes the electromagnetic, weak and strong interactions of the observed elementary particles does however not incorporate gravity. The quantisation of gravity (“quantum gravity”) is a very difficult problem which is presently still far from its soluti...

A little more than half a year before Matrix Mechanics was born, Max Born finished his book Vorlesungen über Atommechanik, Erster Band, which is a state-of-the-art presentation of Bohr-Sommerfeld quantisation. This book, which today seems almost forgotten, is remarkable for its epistemological as well as technical aspects. Here I wish to highlight one aspect in each of these two categories, the...

As a prototype of powerful non-abelian symmetry in an Integrable System, I will show the appearance of a Witt algebra of vector fields in the SG theory. This symmetry does not share anything with the well-known Virasoro algebra of the conformal c = 1 unperturbed limit. Although it is quasi-local in the SG field theory, nevertheless it gives rise to a local action on N -soliton solution variable...

We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i. e. it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantisation without altering the classical limit of the dynamics on the torus, we numerically observe a transition...

We show that several standard associative quantizations can be expressed as cochain module twists in the spirit of Moyal products, at least to O(~), but where the twist element is not a cocycle. This puts such quantisations induced by covariance groups into the setting of our previous work on semiclassicalisation of differential structures where we showed that that noncommutative geometry force...