Operator gauge transformations in nonrelativistic quantum electrodynamics

Thesis/Dissertation · Fri Jan 01 00:00:00 EST 1982

OSTI ID:6760147

Gray, R D

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
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

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