86 research outputs found
Twinlike models with identical linear fluctuation spectra
Recently, the possibility of so-called twinlike field theories has been
demonstrated, that is, of different field theories which share the same
topological defect solution with the same energy density. Further, purely
algebraic conditions have been derived which the corresponding Lagrangians have
to obey in order that the field theories be twins of each other. A further
diagnostical tool which, in general, allows to distinguish the topological
defects of a given theory from the corresponding defects of its twins is the
spectrum of linear fluctuations about these defects. Very recently, however,
explicit examples of twin theories have been constructed such that not only
their shapes and energy densities coincide, but also their linear fluctuation
spectra are the same. Here we show that, again, there exist purely algebraic
conditions for the Lagrangian densities which imply that the corresponding
field theories are twins and that the fluctuation spectra about their defects
coincide. These algebraic conditions allow to construct an infinite number of
twins with coinciding fluctuation spectra for a given theory, and we provide
some explicit examples. The importance of this result is related to the fact
that coinciding defects with coinciding energy densities and identical
fluctuation spectra are almost indistinguishable physically, that is,
indistinguishable in a linear or semiclassical approximation. This implies that
the measurable physical properties of a kink, in general, do not allow to
determine the theory which provides the kink uniquely. Instead, in principle an
infinite number of possible theories has to be considered.Comment: Latex, 13 pages, no figure
Expansion in the Width and Collective Dynamics of a Domain Wall
We show that collective dynamics of a curved domain wall in a
(3+1)-dimensional relativistic scalar field model is represented by Nambu-Goto
membrane and (2+1)-dimensional scalar fields defined on the worldsheet of the
membrane. Our argument is based on a recently proposed by us version of the
expansion in the width. Derivation of the expansion is significantly
reformulated for the present purpose. Third and fourth order corrections to the
domain wall solution are considered. We also derive an equation of motion for
the core of the domain wall. Without the (2+1)-dimensional scalar fields this
equation would be nonlocal.Comment: 26 pages, LaTeX, no figure
Three-body forces from a classical nonlinear field
Forces in the systems of two opposite sign and three identical charges
coupled to the dynamical scalar field of the signum-Gordon model are
investigated. Three-body force is present, and the exact formula for it is
found. Flipping the sign of one of the two charges changes not only the sign
but also the magnitude of the force. Both effects are due to nonlinearity of
the field equation.Comment: 12 pages, 2 figure
Axial momentum for the relativistic Majorana particle
The Hilbert space of states of the relativistic Majorana particle consists of
normalizable bispinors with real components, and the usual momentum operator can not be defined in this space. For this reason, we introduce the
axial momentum operator, as a new observable for this
particle. In the Heisenberg picture, the axial momentum contains a component
which oscillates with the amplitude proportional to , where is the
energy and the mass of the particle. The presence of the oscillations
discriminates between the massive and massless Majorana particle. We show how
the eigenvectors of the axial momentum, called the axial plane waves, can be
used as a basis for obtaining the general solution of the evolution equation,
also in the case of free Majorana field. Here a novel feature is a coupling of
modes with the opposite momenta, again present only in the case of massive
particle or field.Comment: 13 pages, improved presentation, change in the titl
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