Consistent description of field theories with non-Hermitian mass terms

Abstract

We review how to describe a field theory that includes a non-Hermitian mass term in the region of parameter space where the Lagrangian is $PT$-symmetric. The discrete symmetries of the system are essential for understanding the consistency of the model, and the link between conserved current and variation of the Lagrangian has to be revisited in the case of continuous symmetries.

References in corpus (6)

• Introduction to PT-Symmetric Quantum Theory
• Dual PT-Symmetric Quantum Field Theories
• A New Class of non-Hermitian Quantum Hamiltonians with PT Symmetry
• Symmetries and conservation laws in non-Hermitian field theories
• Non-Hermitian extension of gauge theories and implications for neutrino physics
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• PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry
• Field Theory of Dissipative Systems with Gapped Momentum States
• Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
• Non-Hermitian gauge field theories and BPS limits
• Complex BPS solitons with real energies from duality
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance
• Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain