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Operator gauge transformations in nonrelativistic quantum electrodynamics

Thesis/Dissertation ·
OSTI ID:6760147

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 Schroedinger 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 Schroedinger 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 Schroedinger 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.

Research Organization:
North Texas State Univ., Denton (USA)
OSTI ID:
6760147
Country of Publication:
United States
Language:
English

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Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHARGED PARTICLES
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EIGENSTATES
ELECTRODYNAMICS
ELECTROMAGNETIC RADIATION
ELECTRONIC EQUIPMENT
ENERGY
EQUATIONS
EQUIPMENT
FIELD THEORIES
GAUGE INVARIANCE
HAMILTONIANS
HARMONIC OSCILLATORS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MAXWELL EQUATIONS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTIZATION
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RADIATIONS
SCHROEDINGER EQUATION
TIME DEPENDENCE
TRANSFORMATIONS
WAVE EQUATIONS