Spacetime sedeons and their application in relativistic quantum
mechanics and field theory
V.L.Mironov, S.V.Mironov  Spacetime sedeons and their application in relativistic quantum
mechanics and field theory, Institute for Physics of
Microstructures RAS, Nizhniy Novgorod, 2014.
Available also on viXra: http://vixra.org/abs/1407.0068
Russian Version
V.L.Mironov, S.V.Mironov  Spacetime sedeons and their application in relativistic quantum mechanics
and field theory, Institute for Physics of Microstructures
RAS, Nizhniy Novgorod, 2014 (in Russian).
http://ipmras.ru/~Mironov/Publications/SEDEONS.pdf
Sedeonic spacetime algebra
The sedeonic algebra encloses eight groups of
values, which are differed with respect to spatial and time inversion.
Here indexes t and r indicate the transformations (r for
spatial inversion and t for
time inversion), which change the corresponding values. All introduced values
can be integrated into one spacetime object named sedeon, which is defined
by the following expression:
The multiplication and commutation rules for
sedeonic basis elements are presented in tables 1 and 2. In
the tables the value i
is the imaginary unit.
The publications conserning
application of sedeons in field theory
V.L.Mironov, S.V.Mironov  Noncommutative sedeons and their application in
field theory // ArXiv http://arxiv.org/abs/1111.4035
We present sixteencomponent values
"sedeons", generating associative noncommutative spacetime
algebra. The generalized relativistic wave equations based on sedeonic wave
function and spacetime operators are proposed. It is shown that
the sedeonic secondorder wave
equation for massive field can be represented in the form of the system of
Maxwelllike firstorder equations for field's intensities. The sedeonic
firstorder Diraclike equations for massive and massless fields are also
discussed.
V.L.Mironov, S.V.Mironov, S.A.Korolev  Sedeonic theory of massless fields // ArXiv http://arxiv.org/abs/1206.5969
In present paper we develop the description of massless fields on the
basis of spacetime algebra of sixteencomponent sedeons. The generalized
sedeonic secondorder equation for unified gravitoelectromagnetic
(GE) field describing simultaneously gravity and electromagnetism is
proposed. The secondorder relations for the GE field energy, momentum and
Lorentz invariants are derived. We also discuss the sedeonic firstorder
Diraclike equation for the massless field.
S.V.Mironov, V.L.Mironov  Sedeonic theory of massive fields
// ViXra
http://vixra.org/abs/1311.0005
< PDF >
In the present paper we develop the
description of massive fields on the basis of spacetime algebra of
sixteencomponent sedeons. The generalized sedeonic secondorder
equation for the potential of baryon field is proposed. It is shown that
this equation can be reformulated in the form of a system of
Maxwelllike equations for the field intensities. We calculate the
baryonic fields in the simple model of point baryon charge and obtain
the expression for the baryonbaryon interaction energy. We also propose
the generalized sedeonic firstorder equation for the potential of
lepton field and calculate the energies of leptonlepton and
leptonbaryon interactions.
V.L.Mironov, S.V.Mironov  Reformulation of relativistic quantum mechanics
equations with noncommutative sedeons // Applied Mathematics, 4(10C), 5360 (2013).
We present sixteencomponent values
"sedeons", generating associative noncommutative spacetime
algebra. The generalized relativistic wave equations based on sedeonic wave
function and spacetime operators are proposed. We demonstrate that sedeonic
secondorder wave equation for massive field can be reformulated as the
quasiclassical equation for the potentials of the field or in equivalent
form as the Maxwelllike equations for the field intensities. The sedeonic
firstorder Diraclike equations for massive and massless fields are also
discussed.
V.L.Mironov, S.V.Mironov  Sedeonic
equations of gravitoelectromagnetism // Journal of Modern Physics, 5(10), 917927 (2014).
In present paper we develop the
description of massless fields on the basis of spacetime algebra of
sixteencomponent sedeons. The generalized sedeonic secondorder equation for
unified gravitoelectromagnetic (GE) field
describing simultaneously weak gravity and electromagnetism is proposed. The
relations for the GE field energy, momentum and Lorentz invariants are
derived. The special case of GE field described by firstorder sedeonic wave
equation is also discussed.
