Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Gauge transformation properties of a spinor differential operator

Miftachul Hadi

Published Aug 1, 2026• 0 citations
Publisher

Abstract

We introduce a spinor differential operator whose expectation value reproduces the Berry connection exactly. We derive its transformation under local $U(1)$ gauge transformations and show that the conventional Berry gauge transformation follows directly through projection onto the normalized spinor. The proposed formulation provides an operator-level formulation of Berry geometry whose projection reproduces the conventional Berry connection and its gauge transformation.

DOI
10.5281/zenodo.21743042

Related papers

The Berry connection as a projection of a spinor differential operator

Miftachul Hadi

We introduce a matrix-valued spinor differential operator constructed from a normalized spinor field. We show that the Berry connection arises as the expectation value of this operator, providing an alternative operator-theoretic formulation of Berry geometry.

•Aug 1, 2026•0 citations

The algebra of the spinor differential operator in Berry geometry

Miftachul Hadi

We study the algebraic structure of a spinor differential operator associated with the Berry connection, showing that it is a rank-one operator with a simple multiplication law. We establish its relation to the Berry projector through its anti-Hermitian part. These results provide an operator framework for Berry geometry and a basis for future extensions.

•Aug 6, 2026•0 citations

Intrinsic Reconstruction of the Berry Connection from the Spectral Adjoint

Marcus Anderson

The Berry connection of a smoothly varying family of Hermitian operators is conventionally defined through the differentiation of instantaneous eigenvectors, a construction that introduces local gauge choices and becomes singular at energy degeneracies. In this paper we show that the Berry connection admits an intrinsic, gauge-independent reconstruction through the Moore-Penrose pseudoinverse of the adjoint action. By defining the connection directly on the operator level via the spectral adjoint, we eliminate the need to track eigenbases or construct local coordinates. This provides a unified operator formulation that applies equally to non-degenerate and degenerate spectral subspaces.

•Jul 30, 2026•0 citations

Gauge transformation approach to the exact solution of a generalized harmonic oscillator

Fuli Li, Shun-Jin Wang, A. Weiguny +1 more

The exact solution and the invariant operator of a generalized harmonic oscillator are obtained by performing three consecutive gauge transformations on the time-dependent Schrodinger equation. In contrast to previous results, they depend only on solutions of a linear differential equation for the associated classical harmonic oscillator. Non-adiabatic and adiabatic Berry phases for the system are calculated on the basis of the exact solution.

Journal of Physics A Mathematical and General•Feb 7, 1994•39 citations

Weak value vector potential with gauge invariance

Sunkyu Yu, Xianji Piao, Namkyoo Park

The conservation of quantities or dynamics under coordinate transformations, known as gauge invariance, has been the foundation of theoretical frameworks in physics. The finding of gauge-invariant quantities has provided a new way of understanding physical problems, as shown in geometric and topological interpretations of quantum phenomena with the Berry phase, or in the separation of quark and gluon contributions in quantum chromodynamics. Here, focusing on the Berry phase, we extract a new gauge-invariant quantity. By employing different pre- and post-selections in the Berry phase in the context of weak values, we derive the gauge-invariant vector potential from the Berry connection that is originally gauge-dependent, and show that the obtained vector potential corresponds to the weak value of the projected momentum operator in the parameter space. The local nature of this quantity is demonstrated with the Aharonov-Bohm effect, proving that this gauge-invariant vector potential can be interpreted as the only source of the Berry curvature in the magnetic field. This weak value decomposition approach could lead to the identification of new measurable quantities from traditionally unobservable quantities.

•Mar 16, 2020•2 citations

Certain properties of Berry's phases in supersymmetric quantum mechanics. II

K M Cheng, P. C. W. Fung

For pt.I see ibid., vol.25, p.1745 (1992). In the first paper the authors studied certain crucial mathematical properties of Abelian Berry's phases in two quantum systems with supersymmetrically related Hamiltonians. They follow up such investigation by extending their analysis to nonAbelian Berry's phases in this present study. They present the derivation of an explicit expression for the difference in the relevant nonAbelian Berry's connections. Also they have derived an expression for a connection one form, which contain the non-Abelian Berry's connection, and which is invariant in the two supersymmetrically related quantum systems. To illustrate their findings mentioned above, they take the example of a Hamiltonian expressible in spin quadrupole. In this example, with a particular choice of supersymmetric partner, they show that the two Berry's connection one forms of the two supersymmetrically related systems may be related by gauge transformation.

Journal of Physics A Mathematical and General•Aug 21, 1992•1 citation
We introduce a spinor differential operator whose expectation value reproduces the Berry connection exactly. We derive its transformation under local U(1)U(1)U(1) gauge transformations and show that the conventional Berry gauge transformation follows directly through projection onto the normalized spinor. The proposed formulation provides an operator-level formulation of Berry geometry whose projection reproduces the conventional Berry connection and its gauge transformation.
The Berry connection of a smoothly varying family of Hermitian operators is conventionally defined through the differentiation of instantaneous eigenvectors, a construction that introduces local gauge choices and becomes singular at energy degeneracies. In this paper we show that the Berry connection admits an intrinsic, gauge-independent reconstruction through the Moore-Penrose pseudoinverse of the adjoint action. By defining the connection directly on the operator level via the spectral adjoint, we eliminate the need to track eigenbases or construct local coordinates. This provides a unified operator formulation that applies equally to non-degenerate and degenerate spectral subspaces.
The conservation of quantities or dynamics under coordinate transformations, known as gauge invariance, has been the foundation of theoretical frameworks in physics. The finding of gauge-invariant quantities has provided a new way of understanding physical problems, as shown in geometric and topological interpretations of quantum phenomena with the Berry phase, or in the separation of quark and gluon contributions in quantum chromodynamics. Here, focusing on the Berry phase, we extract a new gauge-invariant quantity. By employing different pre- and post-selections in the Berry phase in the context of weak values, we derive the gauge-invariant vector potential from the Berry connection that is originally gauge-dependent, and show that the obtained vector potential corresponds to the weak value of the projected momentum operator in the parameter space. The local nature of this quantity is demonstrated with the Aharonov-Bohm effect, proving that this gauge-invariant vector potential can be interpreted as the only source of the Berry curvature in the magnetic field. This weak value decomposition approach could lead to the identification of new measurable quantities from traditionally unobservable quantities.
For pt.I see ibid., vol.25, p.1745 (1992). In the first paper the authors studied certain crucial mathematical properties of Abelian Berry's phases in two quantum systems with supersymmetrically related Hamiltonians. They follow up such investigation by extending their analysis to nonAbelian Berry's phases in this present study. They present the derivation of an explicit expression for the difference in the relevant nonAbelian Berry's connections. Also they have derived an expression for a connection one form, which contain the non-Abelian Berry's connection, and which is invariant in the two supersymmetrically related quantum systems. To illustrate their findings mentioned above, they take the example of a Hamiltonian expressible in spin quadrupole. In this example, with a particular choice of supersymmetric partner, they show that the two Berry's connection one forms of the two supersymmetrically related systems may be related by gauge transformation.