0
0
*
*
1 2
-;ure 4-5. Double spin-flip, with distant vertex modification. When the two
indicated '. non-filled circles are flipped down there is break in the solid
line at i2 with corresponding local fission and fusion vertex factors. However,
there is also a change in the factors b for the fusion vertex at i\. --':.
distance to the right of spin (i, j) to the next up spin has changed as
well. in other words, "' (it,j) has changed.
4.2.2 Using the Lattice Configurations
We are interested in the physical observables of the, : In :. :'ticular those which
have a direct int. ) on in terms of the field theory described by the Lightcone World
Sheet. Such an observable would be for example the energy levels of the system. To
understand how these will emerge from the world sheet let us consider the system in terms
of time evolution in the discretized Lightcone time x i nair. l our lattice time j. At a
given time j the min can be characterized as a 2M state -.-.um .m with a time
evolution operator T which takes it to the next time j + 1. i negative logarithm of this
:ator is the Hamiltonian of the system, namely the Lightcone P- < .. *ator and the
energy levels are given '. the eigenvalues. '..'.. write T -H, and consider the correlator
between two states (5) and I} :at ed j time steps on a i dic lattice with total
time steps N
(G T T) T (4-16)
Take m) for m N to be the eigenbasis for T with .) = ) and write 0) = In)
and ) I in) then
(E a(b 17)
G(jI I n abti (1A 17)