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arXiv · 1408.2432

Infinitely many inequivalent field theories from one Lagrangian

Carl M. Bender·Daniel W. Hook·Nick E. Mavromatos·Sarben Sarkar
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Abstract

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 $ϕ$. In Euclidean space the Lagrangian of such a theory, $L=\frac{1}{2}(\nablaϕ)^2-igϕ\exp(iaϕ)$, 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 $E_{m,n}\sim(m+1/2)^2a^2/(16n^2)$.

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Carl M. Bender, Daniel W. Hook, Nick E. Mavromatos, Sarben Sarkar. 2014-08-11. Infinitely many inequivalent field theories from one Lagrangian. https://doi.org/10.1103/physrevlett.113.231605

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