PT-Symmetric Quantum Field Theory

In the context of the PT-symmetric version of quantum electrodynamics, it is argued that the C operator introduced in order to define a unitary inner product has nothing to do with charge conjugation.Comment: 4 pages, uses czjphys.cls, to appear in the Proceedings of the 12th International Colloquium on Quantum Groups and Integrable System

Finite-Element Time Evolution Operator for the Anharmonic Oscillator

The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim1/N^2$, where $N$ is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is $H=p^2/2+\lambda q^4/4.$ Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a result for the anharmonic oscillator ground state energy accurate to better than 1\%, while a two-state approximation reduces the error to less than 0.1\%.Comment: Contribution to Harmonic Oscillators II, Cocoyoc, Mexico, March 23-25, 1994, 8 pages, OKHEP-94-01, LaTeX, one uuencoded figur