Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Quantum Chemical Studies on Tropospheric Nucleation Mechanisms Involving Sulfuric Acid

Nucleation is the first step of the process by which gas molecules in the atmosphere condense to form liquid or solid particles. Despite the importance of atmospheric new-particle formation for both climate and health-related issues, little information exists on its precise molecular-level mechanisms. In this thesis, potential nucleation mechanisms involving sulfuric acid together with either water and ammonia or reactive biogenic molecules are studied using quantum chemical methods. Quantum chemistry calculations are based on the numerical solution of Schrödinger's equation for a system of atoms and electrons subject to various sets of approximations, the precise details of which give rise to a large number of model chemistries. A comparison of several different model chemistries indicates that the computational method must be chosen with care if accurate results for sulfuric acid - water - ammonia clusters are desired. Specifically, binding energies are incorrectly predicted by some popular density functionals, and vibrational anharmonicity must be accounted for if quantitatively reliable formation free energies are desired. The calculations reported in this thesis show that a combination of different high-level energy corrections and advanced thermochemical analysis can quantitatively replicate experimental results concerning the hydration of sulfuric acid. The role of ammonia in sulfuric acid - water nucleation was revealed by a series of calculations on molecular clusters of increasing size with respect to all three co-ordinates; sulfuric acid, water and ammonia. As indicated by experimental measurements, ammonia significantly assists the growth of clusters in the sulfuric acid - co-ordinate. The calculations presented in this thesis predict that in atmospheric conditions, this effect becomes important as the number of acid molecules increases from two to three. On the other hand, small molecular clusters are unlikely to contain more than one ammonia molecule per sulfuric acid. This implies that the average NH3:H2SO4 mole ratio of small molecular clusters in atmospheric conditions is likely to be between 1:3 and 1:1. Calculations on charged clusters confirm the experimental result that the HSO4- ion is much more strongly hydrated than neutral sulfuric acid. Preliminary calculations on HSO4- NH3 clusters indicate that ammonia is likely to play at most a minor role in ion-induced nucleation in the sulfuric acid - water system. Calculations of thermodynamic and kinetic parameters for the reaction of stabilized Criegee Intermediates with sulfuric acid demonstrate that quantum chemistry is a powerful tool for investigating chemically complicated nucleation mechanisms. The calculations indicate that if the biogenic Criegee Intermediates have sufficiently long lifetimes in atmospheric conditions, the studied reaction may be an important source of nucleation precursors.