Julian Schwinger: Source Theory and the UCLA Years--- From Magnetic Charge to the Casimir Effect

Julian Schwinger began the construction of Source Theory in 1966 in response to the then apparent failure of quantum field theory to describe strong interactions, the physical remoteness of renormalization, and the utility of effective actions in describing chiral dynamics. I will argue that the source theory development was not really so abrupt a break with the past as Julian may have implied, for the ideas and techniques in large measure were present in his work at least as early as 1951. Those techniques and ideas are still of fundamental importance to theoretical physics, so much so that the designation ``source theory'' has become superfluous. Julian did a great deal of innovative physics during the last 30 years of his life, and I will touch on some of the major themes. The impact of much of this work is not yet apparent. (Invited talk at Washington APS/AAPT meeting)Comment: 15 pages, plain TeX, no figures, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers

Anomalies in PT-Symmetric Quantum Field Theory

It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.Comment: 7 pages, uses czjphys.cls, to appear in proceedings of Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physic

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