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Infinitely many inequivalent field theories from one Lagrangian
Logarithmic time-like Liouville quantum field theory has a generalized PT
invariance, where T is the time-reversal operator and P stands for an S-duality
reflection of the Liouville field . In Euclidean space the Lagrangian of
such a theory, , is analyzed
using the techniques of PT-symmetric quantum theory. It is shown that L defines
an infinite number of unitarily inequivalent sectors of the theory labeled by
the integer n. In one-dimensional space (quantum mechanics) the energy spectrum
is calculated in the semiclassical limit and the mth energy level in the nth
sector is given by .Comment: 5 pages, 7 figure
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