Families of particles with different masses in PT-symmetric quantum field theory

Abstract

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.

4 pages, 3 figures

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
• Effective Potential for Complex Langevin Equations

Cited by in corpus (18)

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• Twofold Transition in PT-Symmetric Coupled Oscillators
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• Infinitely many inequivalent field theories from one Lagrangian
• Taming Dyson-Schwinger equations with null states
• Dyson-Schwinger equations in zero dimensions and polynomial approximations
• Mode truncations and scattering in strong fields
• Principle of minimal singularity for Green's functions
• Analytic structure of eigenvalues of coupled quantum systems
• CPT-Frames for PT-symmetric Hamiltonians
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• ${\varphi }^n$ trajectory bootstrap
• PT-symmetric interpretation of double-scaling
• Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory
• Green Functions for the Wrong-Sign Quartic
• Time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics