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David M. A. Stuart

Publications and source records attributed to David M. A. Stuart.

3 recordsLinked to original sources
arXiv2026

Hamiltonian quantization of solitons in the $ϕ^4_{1+1}$ quantum field theory

We first carry out the soliton sector quantization of the spatially cut-off $ϕ^4_{1+1}$ theory with double well potential in the semiclassical limit, deriving the nonrelativistic Schrödinger equation as an equation describing the limiting soliton dynamics. In the process we prove the semiclassical mass shift formula of Dashen, Hasslacher and Neveu, which is interpreted in terms of a unitary equivalence between normal ordered semiclassical quadratic Hamiltonians in two different representations of the Heisenberg relations. Secondly, we consider the $ϕ^4_{1+1}$ theory coupled topologically to an external electromagnetic field and prove the main result, which is an approximation theorem reminiscent of the Born-Oppenheimer method, which describes the nonrelativistic dynamics of the soliton coupled to infinitely many transverse bosonic degrees of freedom, extending the techniques of soliton modulation theory from classical to quantum field theory.

math-ph↗
arXiv2012

The Schwinger model on $S^1$: Hamiltonian formulation, vacuum and anomaly

We present a Hamiltonian formulation of the Schwinger model on the circle in Coulomb gauge as a semi-bounded self-adjoint operator which is invariant under the modular group ${\cal M}=\Z$ of large gauge transformations. There is a nontrivial action of $\cm$ on fermionic Fock space $\mcH_0$ and its vacuum which plays a role analogous to that of the spectral flow in the formalism involving the infinite Dirac sea. The formulation allows (i) a description of the anomaly and its relation to this group action, and (ii) an explicit identification of the interacting vacuum which arises after the destabilization of the non-interacting vacuum in $\mcH_0$.

math-ph↗