Are there physical theories in which notions of particle are used without the concept of force?
I know about gauge bosons, see: http://en.wikipedia.org/wiki/Force_carrier and http://en.wikipedia.org/wiki/Fundamental_interaction.
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$\begingroup$ I reworded your question to hopefully make it more clear; is the question still asking what you want? $\endgroup$– BMSCommented Oct 31, 2014 at 1:48
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$\begingroup$ Actually, Richard Feynman launched his career and eventually developed his version of QED based on his assumption (a hope, really) that particles interacted directly. To Feynman, fields were just a manifestation of how that direct particle-to-particle interaction operates. $\endgroup$– Terry BollingerCommented Oct 31, 2014 at 2:00
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$\begingroup$ BMS, exactly that. I like your revision. $\endgroup$– tesgoeCommented Oct 31, 2014 at 8:33
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1 Answer
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Quantum field theories have no direct notion of force, neither in the "physical approach" through a Lagrangian and the path integral, nor in the "mathematical approach" through Wightman, Haag-Kastler or other axioms.
The theory of "force carriers" is developed without ever appealing to forces - one imposes a local gauge symmetry upon the theory and discovers that a new notion of derivative is needed, leading in turn to the introduction of a new field, the gauge field, whose quanta are the gauge bosons. From this theory you may obtain the classical notion of force through the non-relativistic limit of the tree-level Feynman diagram between two particles charged under that symmetry.1 But that is not the whole story - the interaction between the gauge field and the matter fields is far more than just that one diagram, more than just that force.
Also, note that particles are not the fundamental notion of QFTs - they are certain excitations of the fields, and it is possible to have field excitations that are relevant that are not particles, e.g. instantons.
1Of course, we are interested in such quantum gauge theories because we know they lead to classical forces, but nothing in their quantum description is dependent on that notion.
answered Oct 31, 2014 at 13:16