Scuseria, Gustavo E2019-05-172019-05-172018-052018-03-02May 2018Zhao, Jinmo. "Symbolic solution for computational quantum many-body theory development." (2018) Diss., Rice University. <a href="https://hdl.handle.net/1911/105668">https://hdl.handle.net/1911/105668</a>.https://hdl.handle.net/1911/105668Computational many-body theories in quantum chemistry, condensed matter, and nuclear physics aim to provide sufficiently accurate description of and insights into the motion of many interacting particles. Due to their intrinsic complexity, the development of such theories generally involves very complex, tedious, and error-prone symbolic manipulations. Here a complete solution to automate the symbolics in many-body theory development is attempted. General data structures based on an existing computer algebra system are designed to specifically address the symbolic problems for which there is currently no satisfactory handling. Based on the data structures, algorithms are given to accomplish common symbolic manipulations and simplifications. Noncommutative algebraic systems, tensors with symmetry, and symbolic summations can all enjoy deep simplifications efficient enough for theories of very complex form. After the symbolic derivation, novel algorithms for automatic optimization of tensor contractions and their sums are devised, which can be used together with automatic code generation tools. In this way, the burden of symbolic tasks in theory development can be vastly reduced, with the potential to spare scientists more time and energy for the actual art and science of many-body theories.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Computer algebramany-body theoryThesis2019-05-17