Quantum Field Theory (QFT) is fundamentally defined by its scale-dependent degrees of freedom situated between ultraviolet and infrared cutoffs, allowing for multiple distinct representations that describe identical correlation functions at the same length scale via duality transformations. This theoretical framework operates within many-body physics to demonstrate that a single physical system can be equivalently described by completely different sets of local operators or actions without altering observable outcomes. Consequently, dualities serve as rigorous mathematical mechanisms linking disparate field theories, such as mapping Ising lattice models onto emergent electromagnetic descriptions in specific dimensional limits.
Quantum Field Theory (QFT) is fundamentally defined by its scale-dependent degrees of freedom situated between ultraviolet and infrared cutoffs, allowing for multiple distinct representations that de…