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  Potential of S-Matrix Theory to lead to breakthrough in GUT

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I was told by a former physicist that he thinks that the now dormant S-Matrix Theory has the potential to lead to a breakthrough in formulating a Grand Unified Theory. He stated several reasons for this; all of which I do not remember except for one: The non-linearity of the differential equations that constitute it could mean that we could apply Dynamical Systems Theory to it, which could lead to a breakthrough in the unification of QM and GR.

  1. Can anyone add this or elucidate on why this theory has this potential, and what would be the potential avenues for exploring it?

  2. Also, can anyone give me a basic intro or summary of S-Matrix theory?

This post imported from StackExchange Physics at 2014-08-06 13:20 (UCT), posted by SE-user Colin
asked Aug 5, 2014 in Theoretical Physics by Colin (20 points) [ no revision ]

1 Answer

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This physicist remembers the radical S-matrix ideas of the 1960s. At the time, because quantum field theory looked superficially sick, the S-matrix ideas were hyped up to lead inexorably to a theory of everything. The hype in this case was justified, they do, but when asymptotically free field theory was discovered and shown to be ok at all scales, there was a political purge, and all the S-matrix people were kicked out, even though they were completely justified.

The S-matrix program culminated in the construction of string theory in 1968, and from this point on, the S-matrix self-consistency ideas became synonymous with string theory. The consistency conditions discovered since then make it reasonable that the only reasonable complete realization of S-matrix ideas in a fundamental theory is some version of string theory. So the field is not at all dormant. String theory is the most active part of high energy physics for at least 30 years.

The reason it seems to be dormant is political. Modern string theorists, for political reasons, no longer talk about their founders, due to misplaced embarrassment. They should not be ashamed of being the intellectual descendents of the S-matrix people, rather they should be ashamed of how they treated these people back when they were still field theorists.

The basic principle of the S-matrix approach is that you don't single out fundamental particles and write down a field Lagrangian, rather you write down an S-matrix expansion using physical states only, none of which can be interpreted as elementary states (a longer sketch see this: http://physicsoverflow.org/21564/what-are-bootstraps?show=21564#q21564). Since you don't have elementary fields, you can't write down a field operators or a Lagrangian, so the way in which you formulate such a theory is to postulate certain Regge trajectories as a leading order approximation, and declare that their interactions must be consistent with Regge theory predictions for trajectory exchange, so that the scattering is appropriately soft at high energies: the large angle scattering falls of exponentially, showing that the objects do not resolve to pointlike constituents. This condition is extremely restrictive, if you don't keep an infinite tower of excitations, you always resolve into points at some scale.

The "nonlinear" part is the unitarity constraint, which tells you how to make loops from tree level scattering. The "systems level" aspect of this is ultimately the requirement that the interactions must keep the leading order scattering consistent with the Regge theory predictions for the exchange of a trajectory.

The theory constructed in this manner just assumed that the Regge trajectories are linear, so that it is clear that the theory is the oscillation of a string. Then the consistency conditions could be solved and you get string worldsheet theories. String theory interactions were constructed and interpreted in this approach, and produce a non-field-theory theory of everything. Now, we have lots of gravitational duals with reconstructed spacetime, which come from string theory, and each of these things is a realization of the S-matrix idea. In the AdS spaces, the analog of the S-matrix is the boundary conformal field theory, so AdS/CFT is a precise modern analog and extension of 1960s S-matrix ideas.

The project succeeded, we have string theory, this fellow seems not to have noticed.

answered Aug 6, 2014 by Ron Maimon (7,730 points) [ revision history ]
edited Aug 7, 2014 by Arnold Neumaier

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