Self-field theory compared with collision theory

[tfleming]

Examining my copy of Heisenberg's 1966 Interscience text "introduction to the unified field theory of elementary particles", he describes how for free-particles one can use linear field theory based on the klein-gordon equation but because this is the IN or OUT of the S matrix theory it's not very useful, and we need a non-linear field equation to solve the collision dynamics.

BUT has anybody got some on-line references to the linear theory i can use please?

i'm chasing down the self-field avenue and want to compare apples and oranges if i can

 

[marlon]

Strange...i was under the impression that non-linear field theories are only necessary when the gauge bosons interact with each other like QCD...

marlon

 

[tfleming]

Strange...i was under the impression that non-linear field theories are only necessary when the gauge bosons interact with each other like QCD...

marlon

yes, that right, that WAS his ultimate context; he was saying in the introduction to the maths (ch.2) that the linear theory could be used to help define the IN and OUT particles but that you needed the non-linear theory for QCD although i' don't think the word had been coined yet (in 1966) ;

i'm wanting to use self-field theory and compare it with the free particle structures ;

 

[humanino]

Non-linear field theories, like Born-Infeld electrodynamics, are presented for instance here :
The nonlinear field theory I. The Dirac electron theory as approximation of the nonlinear electrodynamics
The nonlinear field theory II. The field representation of the Dirac electron theory
The non-linear field theory III: Geometrical illustration of the electromagnetic representation of Dirac's electron theory

I apologize to you tfleming, but I do not fully understand your question.
The S-matrix gives amplitudes between well-defined free-particle asymptotic states. It can and does indeed describe collisions and scattering processes, independent of the fact that the underlying theory is linear or non-linear.

 

[tfleming]

many thanks for that humanino much appreciated; ok, then what makes the collision or scatteriong process non-linear and linear? is it a whether its a 'deep' or 'small' deviation? for instance if you have two particles going in and two coming out that might (or might not?) be linear, but 2 in 3 out would be definitely non-linear?

P.S. i think I've just understood what you're asking me-his didactic method was to discuss the linear maths first ch. 2 and then go on to the non-linear, more complex maths in ch. 3. i'd STILL be interested in what exactly makes a collision linear or non-linear.

cheers Tony

 

[tfleming]

many thanks for that humanino much appreciated; ok, then what makes the collision or scatteriong process non-linear and linear? is it a whether its a 'deep' or 'small' deviation? for instance if you have two particles going in and two coming out that might (or might not?) be linear, but 2 in 3 out would be definitely non-linear?

P.S. i think I've just understood what you're asking me-his didactic method was to discuss the linear maths first ch. 2 and then go on to the non-linear, more complex maths in ch. 3. i'd STILL be interested in what exactly makes a collision linear or non-linear.

cheers Tony

i guess this seems like particle physics 101 to you guys, but it's important to sorting out IF and when a linearized version of self-field theory can be used.
i went back to Jackson's book on 'classical electromagnetics' and he talks about when EM becomes non-linear, such as inside the atom. more as i read on.

 

[tfleming]

this question of mine about self-field theory may allow us to go beyind the common or garden point particle; if a particle has an internal structure then it's not a point particle; so in addition to string theory say, we have another avenue that doesn't necassarily lead to quantum problems such as renormalization.

 

[marlon]

this question of mine about self-field theory may allow us to go beyind the common or garden point particle; if a particle has an internal structure then it's not a point particle; so in addition to string theory say, we have another avenue that doesn't necassarily lead to quantum problems such as renormalization.

Hi, ...

I really don't see how you can make such conclusions on these "quantum problems"

Sounds quite speculative to me...


regards
marlon

 

[tfleming]

well, first of all, g'day marlon, glad to see you alive and kicking;

what i mean is that a point-particle at the origin is going to have problems, 'cos of infinities as we all know via quantum theory and renormalization ( any point particle at zero is by definition dogged by problems. BUT if we can go further and spell out some dynamic structure such that the particles aren't at the origin, then we may not have the same problems. (the 'quantum problems' being these infinities).

i am looking at the possibility that self-fields via linear theory can be helpful to give us the internal structure of particles that are usually dealt with within the non-linear theory.

cheers Tony

 

[tfleming]

forgot to mention; years ago i read a text by R.W.King (from memory) and it was all about 'electromagnetic' or elastic collisions between particles; I'm going to find it within the garage somewhere and drag it out; i think it'll tell me when a collision becomes 'inelastic'; seems to me this must be relevant to string theory somehow??