College of Liberal Arts & Sciences

# Mathematical Physics Seminar

**Abstract: **When quantizing a classical system, one is typically concerned with representing the generalized coordinates *q _{i}* and conjugate momenta

*p*as operators

_{i}*q̂*which act on some Hilbert space, and satisfy the canonical commutation relations,

_{i}and p̂_{j}*[q̂*i

_{i }, p̂_{j}] =*δ*. For a finite number of coordinates and momenta these representations are all unitarily equivalent. However, for theories with an infinite number of

_{ij}*q̂*, such as those found in Quantum Field Theory, there exists infinitely many inequivalent representations.

_{i}’s and p̂_{j }sIn 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.