Dublin Quantum Field Theory Seminar

                            Synge Lecture Theatre
                    School of Mathematics, Hamilton Building
                             Trinity College Dublin

                                 Time: 4.15 pm

April 22        Niall O Murchadha (Dept. of Physics, UCC, Cork)
 
Relativity without relativity; emergent time in classical field theory


Short Abstract: In this talk I will introduce a novel form of
 time-reparametrisation invariant action. This action is both
 overconstrained and underdetermined. The action acts as a filter of
 theories on any chosen configuration space. Any solution must have `hidden'
 symmetries, extra symmetries that are not apparent in the action itself. If
 we choose the space of three-metrics as the configuration space we get
 general relativity, if we add a three-vector we get the Maxwell field, if
 we have several interacting vector fields, they must satisfy the Yang-Mills
 equations. In each case we go from a low symmetry action to a high symmetry
 solution just by demanding that the action is self-consistent.
 Most of the talk will be devoted to a particle model which illustrates in a
 concrete fashion the marvellous properties of this action.

Long Abstract Jacobi introduced a parameter time action, called
 the Jacobi Principle, of the form $\sqrt{E - V}\sqrt{T}$ in particle
 mechanics, where $E$ is a constant, the total energy, $V$ is the
 potential energy, and $T$ the kinetic energy. He showed that it
 reproduced all of the standard equations but with an emergent time. I
 will consider an action quite like the Jacobi Principle but I will
 take the square roots of the individual kinetic energies of each
 particle and then sum. This is still reparametrisation invariant. This
 new action has a large set of constraints which are not mirrored by
 any symmetry of the action, and thus is not, in general,
 self-consistent. What it does do is act as a filter. If the particles
 do not interact everything works beautifully. The `missing' symmetries
 appear in the solution because each particle trajectory turns out to
 be independently reparametrisable. The action has only a global time
 reparametrisation but the solutions have local time
 reparametrisation. This local square root action can be easily
 generalised to field theories and one can use it to pick out each of
 the standard fields of modern classical physics. If we choose the
 space of three-metrics as the configuration space we get general
 relativity, if we add a three-vector we get the Maxwell field, if we
 have several interacting vector fields, they must satisfy the
 Yang-Mills equations. In each case we go from a low symmetry action to
 a hig symmetry solution just by demanding that the action is
 self-consistent.


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Last changed 9 Apr 2002.