Free scalar field theory on a Sobolev space over a bounded interval
High Energy Physics - Theory
2024-05-29 v1 General Relativity and Quantum Cosmology
Abstract
This paper discusses several functional analytic issues relevant for field theories in the context of the Hamiltonian formulation for a free, massless, scalar field defined on a closed interval of the real line. The fields that we use belong to a Sobolev space with a scalar product. As we show this choice is useful because it leads to an explicit representation of the points in the fibers of the phase space (the cotangent bundle of the configuration space). The dynamical role of the boundary of the spatial manifold where the fields are defined is analyzed.
Keywords
Cite
@article{arxiv.2405.17996,
title = {Free scalar field theory on a Sobolev space over a bounded interval},
author = {J. Fernando Barbero G.},
journal= {arXiv preprint arXiv:2405.17996},
year = {2024}
}
Comments
19 pages