Infinitely many inequivalent field theories from one Lagrangian

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

5 pages, 7 figures

References in corpus (6)

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Cited by in corpus (7)

• Symmetries and conservation laws in non-Hermitian field theories
• On the consistency of a non-Hermitian Yukawa interaction
• Towards perturbative renormalization of ${\varphi }^2(i\varphi {)}^{\epsilon }$ quantum field theory
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Original study of the $g{\varphi }^2(i\varphi {)}^{\epsilon }$ theory. Analysis of all orders in $\epsilon$ and resummations
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics
• Non-linear and weak-coupling expansion in Quantum Field Theory