Potential fields and the generalized gauge transformation in the theory of spin particles

We study interference effects in the dynamics of a spin- $1/2$ particle propagating in two dimensions in a disordered potential and subject to a generalized spin-orbit coupling. With the particle initially in a spin-polarized plane wave state, in the short-time regime, before the spin and momentum distributions reach their steady states, we observe a transient backscattering peak offset from the exact backscattering direction, coexisting with a coherent backscattering dip. We present an intuitive explanation of this momentum offset using a non-Abelian gauge transformation. We also describe the full time evolution of the transient peak, from its buildup to its decay with a precise prediction of the dephasing time within a perturbative framework for multiple scattering. Our results can be applied to general spatially uniform SU(2) gauge fields, including the synthetic gauge field in ultracold atoms.We study interference effects in the dynamics of a spin-$1/2$ particle propagating in two dimensions in a disordered potential and subject to a generalized spin-orbit coupling. With the particle initially in a spin-polarized plane wave state, in the short-time regime, before the spin and momentum distributions reach their steady states, we observe a transient backscattering peak offset from the exact backscattering direction, coexisting with a coherent backscattering dip. We present an intuitive explanation of this momentum offset using a non-Abelian gauge transformation. We also describe the full time evolution of the transient peak, from its buildup to its decay with a precise prediction of the dephasing time within a perturbative framework for multiple scattering. Our results can be applied to general spatially uniform SU(2) gauge fields, including the synthetic gauge field in ultracold atoms.

arXiv:2509.07312Physical Review AMar 20, 20262 citations

Operator Gauge Transformations in Nonrelativistic Quantum Electrodynamics

Raymond Dale Gray

A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.

Dec 1, 19820 citations

The temperature-dependent non-Abelian gauge potential

Zheng-Chuan Wang

This study shows that the usual time evolution operator can act as a U(1) gauge transformation on the initial wavefuntion. When considering the spin freedom in the system, the time evolution operator corresponds to a non-Abelian SU(2) gauge transformation for spin-1/2 particles and a SU(3) gauge transformation for spin-1 particles. If we adopt the adiabatic approximation in the magnetization dynamics of a ferromagnetic system driven by a spin-polarized current, a temperature-dependent non-Abelian thermal gauge potential will appear. We can employ a temperature-dependent Landau-Lifshitz-Gilbert (LLG) equation to describe the magnetization dynamics in the semi-classical limit, a linear approximated solution for this equation is given analytically.This study shows that the usual time evolution operator can act as a U(1) gauge transformation on the initial wavefuntion. When considering the spin freedom in the system, the time evolution operator corresponds to a non-Abelian SU(2) gauge transformation for spin-1/2 particles and a SU(3) gauge transformation for spin-1 particles. If we adopt the adiabatic approximation in the magnetization dynamics of a ferromagnetic system driven by a spin-polarized current, a temperature-dependent non-Abelian thermal gauge potential will appear. We can employ a temperature-dependent Landau-Lifshitz-Gilbert (LLG) equation to describe the magnetization dynamics in the semi-classical limit, a linear approximated solution for this equation is given analytically.

quant-pharXiv:2608.25437Aug 27, 2026

The Method of Gauge Transformation in Random Spin Systems

之康尾関, Yukiyasu Ozeki

Jan 1, 19960 citations

Theory of Spin Lattices and Lattice Gauge Models

J. W. Clark, MANFRED L. RISTIG

Springer eBooksJan 1, 19979 citations

We study interference effects in the dynamics of a spin-

1/2

particle propagating in two dimensions in a disordered potential and subject to a generalized spin-orbit coupling. With the particle initially in a spin-polarized plane wave state, in the short-time regime, before the spin and momentum distributions reach their steady states, we observe a transient backscattering peak offset from the exact backscattering direction, coexisting with a coherent backscattering dip. We present an intuitive explanation of this momentum offset using a non-Abelian gauge transformation. We also describe the full time evolution of the transient peak, from its buildup to its decay with a precise prediction of the dephasing time within a perturbative framework for multiple scattering. Our results can be applied to general spatially uniform SU(2) gauge fields, including the synthetic gauge field in ultracold atoms.