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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Unified approach to quantum and classical dualities.

E Cobanera¹, G Ortiz, Z Nussinov

¹Department of Physics, Indiana University, Bloomington, Indiana 47405, USA.

Physical Review Letters

|April 7, 2010

Summary

This study introduces a novel method to systematically establish classical, quantum, and emergent dualities using quantum Hamiltonian bond algebra morphisms. This approach derives dual variables and reveals new self-dualities in four-dimensional Abelian gauge field theories.

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Area of Science:

Theoretical Physics
Quantum Field Theory
Mathematical Physics

Background:

Dualities are fundamental concepts in physics, relating different theories or phases.
Identifying and establishing dualities, especially emergent ones, remains a significant challenge.
Previous methods for deriving dual variables were often based on intuition or guesswork.

Purpose of the Study:

To develop a systematic method for unveiling and establishing classical, quantum, and emergent dualities.
To provide a rigorous framework for deriving dual variables.
To explore new duality relations in quantum field theories.

Main Methods:

Utilizing morphisms of the bond algebra of a quantum Hamiltonian.
Characterizing dualities as unitary mappings implementing these morphisms.
Analyzing the properties of even powers of these unitary mappings as symmetries.

Main Results:

A systematic procedure for establishing dualities is presented.
Dual variables are rigorously derived within the developed formalism.
New self-dualities are discovered for four-dimensional Abelian gauge field theories.

Conclusions:

The proposed method offers a powerful tool for understanding dualities in various physical theories.
The formalism provides a pathway to discover and verify new duality relations.
This work advances the study of quantum field theories and their symmetries.