Dartmouth Events

Physics & Astronomy - Senior Honor Thesis - Shadi Ali Ahmad, Dartmouth College

Title: "Relative subsystems and entanglement in gauge theory”

Thursday, May 26, 2022
3:00pm – 4:00pm
Wilder 104
Intended Audience(s): Public
Categories: Lectures & Seminars

Abstract: The most basic notion in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In standard quantum mechanical systems, this partitioning is encoded in the tensor product structure of the Hilbert space of the system. However, for quantum field theories, this tensor product structure fails due to the universal divergence of the entanglement entropy, and so subsystems must be identified with commuting subalgebras of observables that encode a notion of locality. In canonical approaches to quantum gravity, this algebraic construction is complicated by the fact that gauge-invariant observables are inherently non-local and can be difficult to construct in practice. For a quantum theory with gauge constraints, we prove that while the unconstrained (kinematical) Hilbert space may admit a tensor product structure, the physical (gauge-invariant) Hilbert space need not inherit this tensor product structure upon implementation of the constraints. We completely characterize the necessary and sufficient conditions for the physical Hilbert space to inherit the kinematical subsystem structure. We review and subsequently leverage the framework of quantum reference frames to show that different reference frames induce generically different subsystem algebras of observables. The main result of this work is the identification of a gauge-invariant but frame-dependent notion of subsystems and entanglement in gauge theories.


Join Zoom Meeting

Meeting ID: 983 8946 4441
Passcode: Ahmad

For more information, contact:
Tressena Manning

Events are free and open to the public unless otherwise noted.