Journal of Nonlinear Mathematical Physics

<Previous Article In Issue
Next Article In Issue>
Volume 18, Issue 2, June 2011, Pages 291 - 297

Exact Solutions of Classical Scalar Field Equations

Authors
Marco Frasca
Via Erasmo Gattamelata, 3, 00176 Roma, Italy,marcofrasca@mclink.it
Received 17 May 2010, Accepted 30 November 2010, Available Online 7 January 2021.
DOI
10.1142/S1402925111001441How to use a DOI?
Keywords
Exact solutions; quartic scalar field theory; mass gap
Abstract

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first-order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 2
Pages
291 - 297
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001441How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Marco Frasca
PY  - 2021
DA  - 2021/01/07
TI  - Exact Solutions of Classical Scalar Field Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 291
EP  - 297
VL  - 18
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001441
DO  - 10.1142/S1402925111001441
ID  - Frasca2021
ER  -