Duality family of scalar field

Abstract

We show that there exists a duality family of self-interacting massive scalar fields. The scalar field in a duality family are related by a duality transformation. Such a duality of scalar fields is a field version of the Newton-Hooke duality in classical mechanics. The duality transformation preserves the type of the field equation: transforming a Klein-Gordon type equation to another Klein-Gordon type equation with a different self-interacting potential. Once a field in a duality family is solved, all other family members are solved by the transformation. That is, a series of exactly solvable models can be constructed from one exactly solvable model. The dual field of the power-interaction field, the sine-Gordon field, etc., are considered. Moreover, as a comparison, we show an analogue of the duality in classical and quantum mechanics.

References in corpus (44)

• Large N Field Theories, String Theory and Gravity
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Nonlinear Fluid Dynamics from Gravity
• Heat kernel expansion: user's manual
• Target Space Duality in String Theory
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• An Introduction to T-Duality in String Theory
• From Navier-Stokes To Einstein
• Digital Quantum Simulation of Minimal AdS/CFT
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Forced Fluid Dynamics from Gravity
• Four-Dimensional String/String Duality
• Deep Learning and AdS/CFT
• Boundary conditions for General Relativity on AdS${}_3$ and the KdV hierarchy
• A note on spin-s duality
• The holographic fluid dual to vacuum Einstein gravity
• Chaotic strings in AdS/CFT
• Measurement of the underlying event in the Drell-Yan process in proton-proton collisions at sqrt(s) = 7 TeV
• The relativistic fluid dual to vacuum Einstein gravity
• Electric-Magnetic Duality Invariant Lagrangians
• The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm
• The number of eigenstates: counting function and heat kernel
• The most general axially symmetric electrovac spacetime adimitting separable equations of motion
• Towards a general fluid/gravity correspondence
• A spacetime dual to the NUT spacetime
• Dual geometries and spacetime singularities
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Fluid/Gravity Correspondence For General Non-rotating Black Holes
• Neutron-proton mass difference from gauge/gravity duality
• Electric-Magnetic Duality in QED Effective Action
• Heat-kernel approach for scattering
• Electric-Magnetic Duality Rotations and Invariance of Actions
• Electromagnetic duality in general relativity
• Thermodynamics and gauge/gravity duality for Lifshitz black holes in the presence of exponential electrodynamics
• A duality relation for fluid spacetime
• A strong-weak coupling duality between two perturbed quantum many-body systems: CSS codes and Ising-like systems
• An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
• Gravoelectric-dual of the Kerr solution
• Forced Fluid Dynamics from Gravity in Arbitrary Dimensions
• Flat space compressible fluid as holographic dual of black hole with curved horizon
• Lattice sine-Gordon model
• Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of $1+1$-Dimensional Bosonization
• A duality of fields

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• Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate
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• Scattering approach for calculating one-loop effective action and vacuum energy
• A duality in classical and quantum mechanics: General results