Quantization of the ModMax Oscillator

Abstract

We quantize the ModMax oscillator, which is the dimensional reduction of the Modified Maxwell theory to one spacetime dimension. We show that the propagator of the ModMax oscillator satisfies a differential equation related to the Laplace equation in cylindrical coordinates, and we obtain expressions for the classical and quantum partition functions of the theory. To do this, we develop general results for deformations of quantum mechanical theories by functions of conserved charges. We show that canonical quantization and path integral quantization of such deformed theories are equivalent only if one uses the phase space path integral; this gives a precise quantum analogue of the statement that classical deformations of the Lagrangian are equivalent to those of the Hamiltonian.

63 pages; LaTeX

References in corpus (5)

• Solving the Simplest Theory of Quantum Gravity
• On p-form gauge theories and their conformal limits
• Maximally symmetric nonlinear extension of electrodynamics and charged particles
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• A supersymmetric nonlinear sigma model analogue of the ModMax theory

Cited by in corpus (8)

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• Flows in the Space of Interacting Chiral Boson Theories
• Waves and strings in an interacting conformal chiral 2-form theory in six dimensions
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
• Bound states around vacuum in scalar ModMax model