Richard Shurtleff - Academia.edu (original) (raw)
Papers by Richard Shurtleff
The Lie algebra of a Lie group is a set of commutation relations, equations satisfied by the grou... more The Lie algebra of a Lie group is a set of commutation relations, equations satisfied by the group's generators. For SU(2) and many other Lie groups, the equations have been solved and matrix generators are realized as algebraic expressions suitable for further investigation or numerical evaluation. This article presents formulas that give a set of matrix generators for any irreducible representation of the group SU(3), the group of unimodular unitary threedimensional complex matrices with matrix multiplication. To assist in calculating the matrix generators, a Mathematica computer program and a Fortran 90 program are included.
By adding generalizations involving translations, the machinery of the quantum theory of free fie... more By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.
viXra, 2019
Electric charges may have mass in part or in full because they charged. Supplying details is the ... more Electric charges may have mass in part or in full because they charged. Supplying details is the electromagnetic mass problem. Here, the charge's mass is associated with intrinsic quantum mechanical quantities so that the classical problems with extended charge distributions, for example, are irrelevant. An intrinsic vector potential is defined, based on intrinsic linear momentum. The charge-electromagnetic field interaction energy is gauge-dependent and the needed mass term is placed with the interaction energy in the intrinsic gauge. Traditional electromagnetism retains its gauge invariance. The field equations make no new predictions since all dynamic dependence on intrinsic quantities can be gauged away. The field equations describe a massive, charged 4-spinor Dirac electron-like particle and an uncharged, massless neutrino-like particle, formulas that have been a part of physics for nearly a century.
By adding generalizations involving translations, the machinery of the quantum theory of free fie... more By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.
The Lie algebra of a Lie group is a set of commutation relations, equations satisfied by the grou... more The Lie algebra of a Lie group is a set of commutation relations, equations satisfied by the group's generators. For SU(2) and many other Lie groups, the equations have been solved and matrix generators are realized as algebraic expressions suitable for further investigation or numerical evaluation. This article presents formulas that give a set of matrix generators for any irreducible representation of the group SU(3), the group of unimodular unitary threedimensional complex matrices with matrix multiplication. To assist in calculating the matrix generators, a Mathematica computer program and a Fortran 90 program are included.
By adding generalizations involving translations, the machinery of the quantum theory of free fie... more By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.
viXra, 2019
Electric charges may have mass in part or in full because they charged. Supplying details is the ... more Electric charges may have mass in part or in full because they charged. Supplying details is the electromagnetic mass problem. Here, the charge's mass is associated with intrinsic quantum mechanical quantities so that the classical problems with extended charge distributions, for example, are irrelevant. An intrinsic vector potential is defined, based on intrinsic linear momentum. The charge-electromagnetic field interaction energy is gauge-dependent and the needed mass term is placed with the interaction energy in the intrinsic gauge. Traditional electromagnetism retains its gauge invariance. The field equations make no new predictions since all dynamic dependence on intrinsic quantities can be gauged away. The field equations describe a massive, charged 4-spinor Dirac electron-like particle and an uncharged, massless neutrino-like particle, formulas that have been a part of physics for nearly a century.
By adding generalizations involving translations, the machinery of the quantum theory of free fie... more By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.