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PT-symmetric quantum field theory with Carl Bender

• The Graduate Center, CUNY (Rm 5209) 365 5th Avenue New York, NY, 10016 United States (map)

1-3pm in Rm 5209

PT-symmetric quantum mechanics began with a study of the Hamiltonian $$H=p^2+x^2(ix)^\epsilon.$$ A surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when $\epsilon\geq0$. This talk examines the corresponding quantum-field-theoretic Hamiltonian $$H=\half(\nabla\phi)^2+\half\phi^2(i\phi)^\epsilon$$
in D-dimensional spacetime, where $\phi$ is a pseudoscalar field. It is shown how to calculate the Green's functions as series in powers of $\epsilon$ directly from the Euclidean partition function. Exact finite expressions for the vacuum energy density, all of the connected n-point Green's functions, and the renormalized mass to order $\epsilon$ are derived for $0\leq D<2$. For $D\geq2$ the one-point Green's function and the renormalized mass are divergent but perturbative renormalization can be performed. The remarkable spectral properties of PT-symmetric quantum mechanics appear to persist in PT-symmetric quantum field theory.