@article{THESIS,
      recid = {12949},
      author = {Du, Yi-Hsien},
      title = {Field Theory of Quantum Matter},
      publisher = {University of Chicago},
      school = {Ph.D.},
      address = {2024-08},
      number = {THESIS},
      abstract = {We present a collection of six stories elucidating the  applications of field theories across diverse topics in  condensed matter theory. These stories are interconnected  by an underlying hidden field theoretical framework,  characterized by symmetries, diffeomorphisms, and  noncommutativity, which are also interlinked and form the  foundational structure of this thesis. The first story  describes the nonlinear bosonization approach which offers  both perturbative and non-perturbative techniques for  studying Fermi and non-Fermi liquids. This approach  naturally leads to a nonlinear multidimensional bosonized  description, with nonlinear corrections fixed by the  geometry of the Fermi surface. The second story highlights  the critical role of volume-preserving diffeomorphisms in  nonabelian higher-rank gauge theories. The third story  explores the noncommutative field theoretical framework of  the fractional quantum Hall effect, emphasizing the  interplay between volume-preserving diffeomorphisms and  noncommutative field theory. Moving forward, the fourth  story extends this exploration to a noncommutative field  theory describing the collective oscillation mode of a  vortex lattice in a two-dimensional rotating Bose-Einstein  condensate. Building on the fourth story, the fifth story  examines broader applications, exploring potential  connections with other condensed matter systems and  generalizing concepts to higher dimensions. Finally, the  sixth story investigates dual formulations of the  previously discussed theories and examines topological  crystalline defects and quantum melting transitions.  Together, these stories provide a comprehensive view of how  field theoretical structure underpins and interconnects  diverse phenomena in condensed matter physics.},
      url = {http://knowledge.uchicago.edu/record/12949},
      doi = {https://doi.org/10.6082/uchicago.12949},
}