Euclidean nonlinear classical field equations with unique vacuum
dc.contributor.author | Williams, David N. | en_US |
dc.contributor.author | Rauch, Jeffrey | en_US |
dc.date.accessioned | 2006-09-11T17:52:49Z | |
dc.date.available | 2006-09-11T17:52:49Z | |
dc.date.issued | 1978-10 | en_US |
dc.identifier.citation | Rauch, Jeffrey; Williams, David N.; (1978). "Euclidean nonlinear classical field equations with unique vacuum." Communications in Mathematical Physics 63(1): 13-29. <http://hdl.handle.net/2027.42/46518> | en_US |
dc.identifier.issn | 0010-3616 | en_US |
dc.identifier.issn | 1432-0916 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46518 | |
dc.description.abstract | We study the real, Euclidean, classical field equation 0$$]]> where φ: ℝ d →ℝ is suitably small at infinity. We study existence and regularity assuming that λ≧0, F ∈ C ∞ (ℝ), and aF ( a )≧0∀ a ∈∝. These hypotheses allow strongly nonlinear F and nonunique solutions for f ≠0. When F′ ≧0, we prove uniqueness, various contractivity properties, analytic dependence on the coupling constant λ, and differentiability in the external source f . For applications in the loop expansion in quantum field theory, it is useful to know that φ is in the Schwartz class L whenever f is, and we provide a proof of this fact. The technical innovations of the problem lie in treating the noncompactness of R d , the strong nonlinearity of F , and the polynomial weights in the seminorms defining L . | en_US |
dc.format.extent | 1091632 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.subject.other | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | en_US |
dc.subject.other | Relativity and Cosmology | en_US |
dc.subject.other | Quantum Computing, Information and Physics | en_US |
dc.subject.other | Statistical Physics | en_US |
dc.subject.other | Quantum Physics | en_US |
dc.title | Euclidean nonlinear classical field equations with unique vacuum | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, The University of Michigan, 48109, Ann Arbor, Michigan, USA | en_US |
dc.contributor.affiliationum | Randall Laboratory of Physics, The University of Michigan, 48109, Ann Arbor, Michigan, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46518/1/220_2005_Article_BF02156127.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF02156127 | en_US |
dc.identifier.source | Communications in Mathematical Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.