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This paper advances fundamental quantum physics by reformulating the Schrödinger equation within a gauge theory framework, unifying hydrodynamic and topological structures relevant to quantum many-body systems. By integrating electromagnetic interactions with Berry and spin connections, the work provides rigorous mathematical tools for analyzing phase holonomy and asymptotic symmetries in acoustic branches of quantum fields. Such theoretical developments are critical for deepening our understanding of the underlying mathematics governing quantum computing architectures and condensed matter simulations.
The Schrodinger Equation as a Gauge Theory
arXiv:2604.26016v3 Announce Type: replace-cross Abstract: The conserved probability current of the Schrodinger field admits a dimension-dependent gauge representation that provides a convenient setting for comparing hydrodynamic, topological and infrared structures. We use this representation to develop a unified treatment of several deformations of the Madelung momentum. BF couplings incorporate electromagnetic interactions, Berry and spin connections, projected non-abelian adiabatic data, and intrinsic phase holonomy within the same framework. In $(2+1)$ dimensions, the Chern-Simons deformation can be reduced to a nonlocal functional of the wavefunction. Its Coulomb-gauge form separates into a phase-sensitive geometric contribution and a density-dependent dynamical contribution; we show explicitly how this separation changes under a general gauge transformation and recover the topological braiding phase in the well-separated adiabatic regime. For systems with a spatial boundary, we derive the equal-time symplectic structure, the associated surface charges, and their boundary algebra. Finally, after a nonlinear interaction produces the Bogoliubov acoustic branch, the radiative memory can be expressed in the dual two-form variables. Its zero-average component is generated by a residual large gauge transformation, whereas the monopole component remains independent global data. This provides a gauge-theoretic description of the memory/asymptotic-symmetry sector of the acoustic infrared structure.
Abstract:The conserved probability current of the Schrodinger field admits a dimension-dependent gauge representation that provides a convenient setting for comparing hydrodynamic, topological and infrared structures. We use this representation to develop a unified treatment of several deformations of the Madelung momentum. BF couplings incorporate electromagnetic interactions, Berry and spin connections, projected non-abelian adiabatic data, and intrinsic phase holonomy within the same framework. In $(2+1)$ dimensions, the Chern-Simons deformation can be reduced to a nonlocal functional of the wavefunction. Its Coulomb-gauge form separates into a phase-sensitive geometric contribution and a density-dependent dynamical contribution; we show explicitly how this separation changes under a general gauge transformation and recover the topological braiding phase in the well-separated adiabatic regime. For systems with a spatial boundary, we derive the equal-time symplectic structure, the associated surface charges, and their boundary algebra. Finally, after a nonlinear interaction produces the Bogoliubov acoustic branch, the radiative memory can be expressed in the dual two-form variables. Its zero-average component is generated by a residual large gauge transformation, whereas the monopole component remains independent global data. This provides a gauge-theoretic description of the memory/asymptotic-symmetry sector of the acoustic infrared structure.
v1: 58 pages; v2: 59 pages, text modified, misprints corrected, results improved; v3: 64 pages, major revision of sections 3.3 and 4, details added, new references added, comments and references are welcome
High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
arXiv:2604.26016 [hep-th]
(or arXiv:2604.26016v3 [hep-th] for this version)
Full text under the publisher's open licence · 245 words
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