Introduction to the Use of Non-Linear Techniques in S-Matrix Theory

David Atkinson

doi:10.1007/978-3-7091-5835-7_2

Introduction to the Use of Non-Linear Techniques in S-Matrix Theory

David Atkinson

High-Energy Frontier

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

I am going to explain to you how one can tackle certain problems in S-matrix theory that involve nonlinear functional equations. A physicist’s usual reaction to a non-linear equation of this kind would be either to try to get an approximate solution by iteration, or to introduce a linearization, perhaps in the neighbourhood of a known approximate solution. I will introduce some concepts of Banach space analysis [1], which will enable us to put these intuitive ideas on a rigorous basis. The advantage is that one can sometimes prove the existence of solutions of the exact equations, without any approximations.

Original language	English
Title of host publication	Developments in High Energy Physics
Subtitle of host publication	Proceedings of the IX. Internationale Universitätswochen für Kernphysik 1970 der Karl-Franzens-Universität Graz
Publisher	Springer
Pages	32-70
Number of pages	39
DOIs	https://doi.org/10.1007/978-3-7091-5835-7_2
Publication status	Published - 1970
Event	Developments in High Energy Physics - Steiermark, Austria Duration: 23-Feb-1970 → 7-Mar-1970

Conference

Conference	Developments in High Energy Physics
Country/Territory	Austria
City	Steiermark
Period	23/02/1970 → 07/03/1970

Access to Document

10.1007/978-3-7091-5835-7_2

Handle.net

Persistent link

Cite this

@inproceedings{e0da52a99fd54c40ad7994256da18190,

title = "Introduction to the Use of Non-Linear Techniques in S-Matrix Theory",

abstract = "I am going to explain to you how one can tackle certain problems in S-matrix theory that involve nonlinear functional equations. A physicist{\textquoteright}s usual reaction to a non-linear equation of this kind would be either to try to get an approximate solution by iteration, or to introduce a linearization, perhaps in the neighbourhood of a known approximate solution. I will introduce some concepts of Banach space analysis [1], which will enable us to put these intuitive ideas on a rigorous basis. The advantage is that one can sometimes prove the existence of solutions of the exact equations, without any approximations.",

author = "David Atkinson",

year = "1970",

doi = "10.1007/978-3-7091-5835-7_2",

language = "English",

pages = "32--70",

booktitle = "Developments in High Energy Physics",

publisher = "Springer",

note = "Developments in High Energy Physics ; Conference date: 23-02-1970 Through 07-03-1970",

}

Atkinson, D 1970, Introduction to the Use of Non-Linear Techniques in S-Matrix Theory. in Developments in High Energy Physics: Proceedings of the IX. Internationale Universitätswochen für Kernphysik 1970 der Karl-Franzens-Universität Graz. Springer, pp. 32-70, Developments in High Energy Physics, Steiermark, Austria, 23/02/1970. https://doi.org/10.1007/978-3-7091-5835-7_2

Introduction to the Use of Non-Linear Techniques in S-Matrix Theory. / Atkinson, David.
Developments in High Energy Physics: Proceedings of the IX. Internationale Universitätswochen für Kernphysik 1970 der Karl-Franzens-Universität Graz. Springer, 1970. p. 32-70.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Introduction to the Use of Non-Linear Techniques in S-Matrix Theory

AU - Atkinson, David

PY - 1970

Y1 - 1970

N2 - I am going to explain to you how one can tackle certain problems in S-matrix theory that involve nonlinear functional equations. A physicist’s usual reaction to a non-linear equation of this kind would be either to try to get an approximate solution by iteration, or to introduce a linearization, perhaps in the neighbourhood of a known approximate solution. I will introduce some concepts of Banach space analysis [1], which will enable us to put these intuitive ideas on a rigorous basis. The advantage is that one can sometimes prove the existence of solutions of the exact equations, without any approximations.

AB - I am going to explain to you how one can tackle certain problems in S-matrix theory that involve nonlinear functional equations. A physicist’s usual reaction to a non-linear equation of this kind would be either to try to get an approximate solution by iteration, or to introduce a linearization, perhaps in the neighbourhood of a known approximate solution. I will introduce some concepts of Banach space analysis [1], which will enable us to put these intuitive ideas on a rigorous basis. The advantage is that one can sometimes prove the existence of solutions of the exact equations, without any approximations.

U2 - 10.1007/978-3-7091-5835-7_2

DO - 10.1007/978-3-7091-5835-7_2

M3 - Conference contribution

SP - 32

EP - 70

BT - Developments in High Energy Physics

PB - Springer

T2 - Developments in High Energy Physics

Y2 - 23 February 1970 through 7 March 1970

ER -

Introduction to the Use of Non-Linear Techniques in S-Matrix Theory

Abstract

Conference

Access to Document

Handle.net

Fingerprint

Cite this