PIRSA:09110001 Scientific Series Quantum Information

DOI10.48660/09110001

Series: Perimeter Institute Quantum Discussions

Ortiz, G. (2009). Unified approach to classical and quantum dualities. Perimeter Institute. https://pirsa.org/09110001

Ortiz, Gerardo. Unified approach to classical and quantum dualities. Perimeter Institute, Nov. 18, 2009, https://pirsa.org/09110001 

@misc{ pirsa_PIRSA:09110001,
  doi = {10.48660/09110001},
  url = {https://pirsa.org/09110001},
  author = {Ortiz, Gerardo},
  keywords = {Quantum Information},
  language = {en},
  title = {Unified approach to classical and quantum dualities},
  publisher = {Perimeter Institute},
  year = {2009},
  month = {nov},
  note = {PIRSA:09110001 see, \url{https://pirsa.org}}
}

Abstract

Dualities appear in nearly all disciplines of physics and play a central role in statistical mechanics and field theory. I will discuss in a pedagogical way our recent findings motivated by a quest for a simple unifying framework for the detection and treatment of dualities. I will explain how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories (i.e. emergent dualities), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables (non-local mappings between the elementary degrees of freedom of the theory) which were guessed in the past can be derived in our formalism. New self-dualities for four-dimensional Abelian gauge field theories will be discussed.

Resources

Next talk

Related Talks