CHAPTER 3. The Wavefunction and the Quantum State

Alisa Bokulich

Traditionally \1 is used to stand for both the mathematical wavefunction (the representation) and the quantum state (thing in the world). This elision has been elevated to a metaphysical thesis by advocates of wavefunction realism. The aim of Chapter 10 is to challenge the hegemony of the wavefunction by calling attention to a littleknown formulation of quantum theory that does not make use of the wavefunction in representing the quantum state. This approach, called Lagrangian quantum hydrodynamics (LQH), is a full alternative formulation, not an approximation scheme. A consideration of alternative formalisms is essential for any realist project that attempts to read the ontology of a theory off the mathematical formalism. The chapter shows that LQH falsifies the claim that one must represent the many-body quantum state as living in 3n-dimensional configuration space. When exploring quantum realism, regaining sight of the proverbial forest of quantum representations beyond the \1 is just the beginning.

N. J. B. Green

This chapter points to the fact that certain quantum-mechanical problems cannot be solved, even with the aid of symmetry. It cites two basic types of approximations, which include the simplification to a form that permits explicit solution and building an accurate computational solution by superposing large numbers of simple wavefunctions. It also explains that approximation must be optimised as it is necessary to have a foolproof way to find the best possible approximation of the assumed form. The chapter talks about expectation energy as the basis of the variation method, which is calculated from an approximate wavefunction that must be greater than the true ground state energy. It attempts to describe a system in its ground state that has an approximate wavefunction which contains a variable parameter.

Alto Osada, Rekishu Yamazaki, Atsushi Noguchi

Juven Wang

In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum systems including symmetry-protected topological states and topologically ordered states. Chapter 1. Introduction. Chapter 2. Geometric phase, wavefunction overlap, spacetime path integral and topological invariants. Chapter 3. Aspects of Symmetry. Chapter 4. Aspects of Topology. Chapter 5. Aspects of Anomalies. Chapter 6. Quantum Statistics and Spacetime Surgery. Chapter 7. Conclusion: Finale and A New View of Emergence-Reductionism. (Thesis supervisor: Prof. Xiao-Gang Wen)