Mathematical Physics Seminar
Abstract: When quantizing a classical system, one is typically concerned with representing the generalized coordinates qi and conjugate momenta pi as operators q̂i and p̂j which act on some Hilbert space, and satisfy the canonical commutation relations, [q̂i , p̂j] = iδij. For a finite number of coordinates and momenta these representations are all unitarily equivalent. However, for theories with an infinite number of q̂i’s and p̂j s, such as those found in Quantum Field Theory, there exists infinitely many inequivalent representations.
In the most common formulation of QFT, these inequivalent representations can be demonstrated by comparing two free massive scalar fields each with a different mass. A similar calculation in the the light-front formulation of QFT does not at first appear to provide the expected inequivalent representations.
This talk will discuss how the inequivalent representations are recovered in the light-front formulation, as well as the role that inequivalent representations play in Quantum Field Theory.