1,773 research outputs found
Orthogonal Decomposition of Some Affine Lie Algebras in Terms of their Heisenberg Subalgebras
In the present note we suggest an affinization of a theorem by Kostrikin
et.al. about the decomposition of some complex simple Lie algebras
into the algebraic sum of pairwise orthogonal Cartan subalgebras. We point out
that the untwisted affine Kac-Moody algebras of types ( prime,
), can be decomposed into
the algebraic sum of pairwise or\-tho\-go\-nal Heisenberg subalgebras. The
and cases are discussed in great detail. Some possible
applications of such decompositions are also discussed.Comment: 16 pages, LaTeX, no figure
Vertex Operators and Soliton Time Delays in Affine Toda Field Theory
In a space-time of two dimensions the overall effect of the collision of two
solitons is a time delay (or advance) of their final trajectories relative to
their initial trajectories. For the solitons of affine Toda field theories, the
space-time displacement of the trajectories is proportional to the logarithm of
a number depending only on the species of the colliding solitons and their
rapidity difference. is the factor arising in the normal ordering of the
product of the two vertex operators associated with the solitons. is shown
to take real values between and . This means that, whenever the solitons
are distinguishable, so that transmission rather than reflection is the only
possible interpretation of the classical scattering process, the time delay is
negative and so an indication of attractive forces between the solitons.Comment: p. 24 Latex, Swansea-SWAT/93-94/3
Poincar\'e recurrence theorem and the strong CP-problem
The existence in the physical QCD vacuum of nonzero gluon condensates, such
as , requires dominance of gluon fields with finite mean action
density. This naturally allows any real number value for the unit ``topological
charge'' characterising the fields approximating the gluon configurations
which should dominate the QCD partition function. If is an irrational
number then the critical values of the parameter for which CP is
spontaneously broken are dense in , which provides for a mechanism
of resolving the strong CP problem simultaneously with a correct implementation
of symmetry. We present an explicit realisation of this
mechanism within a QCD motivated domain model. Some model independent arguments
are given that suggest the relevance of this mechanism also to genuine QCD.Comment: 8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now
includes model independent argument
Dual Projection and Selfduality in Three Dimensions
We discuss the notion of duality and selfduality in the context of the dual
projection operation that creates an internal space of potentials. Contrary to
the prevailing algebraic or group theoretical methods, this technique is
applicable to both even and odd dimensions. The role of parity in the kernel of
the Gauss law to determine the dimensional dependence is clarified. We derive
the appropriate invariant actions, discuss the symmetry groups and their proper
generators. In particular, the novel concept of duality symmetry and
selfduality in Maxwell theory in (2+1) dimensions is analysed in details. The
corresponding action is a 3D version of the familiar duality symmetric
electromagnetic theory in 4D. Finally, the duality symmetric actions in the
different dimensions constructed here manifest both the SO(2) and
symmetries, contrary to conventional results.Comment: 20 pages, late
Helicity, polarization, and Riemann-Silberstein vortices
Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime
where the complex form of a free electromagnetic field given by F=E+iB is null
(F.F=0), and they can indeed be interpreted as the collective history swept out
by moving vortex lines of the field. Formally, the nullity condition is similar
to the definition of "C-lines" associated with a monochromatic electric or
magnetic field, which are curves in space where the polarization ellipses
degenerate to circles. However, it was noted that RS vortices of monochromatic
fields generally oscillate at optical frequencies and are therefore
unobservable while electric and magnetic C-lines are steady. Here I show that
under the additional assumption of having definite helicity, RS vortices are
not only steady but they coincide with both sets of C-lines, electric and
magnetic. The two concepts therefore become one for waves of definite frequency
and helicity. Since the definition of RS vortices is relativistically invariant
while that of C-lines is not, it may be useful to regard the vortices as a
wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on
Singular Optics; minor changes from v.
Non-universal scalar-tensor theories and big bang nucleosynthesis
We investigate the constraints that can be set from big-bang nucleosynthesis
on two classes of models: extended quintessence and scalar-tensor theories of
gravity in which the equivalence principle between standard matter and dark
matter is violated. In the latter case, and for a massless dilaton with
quadratic couplings, the phase space of theories is investigated. We delineate
those theories where attraction toward general relativity occurs. It is shown
that big-bang nucleosynthesis sets more stringent constraints than those
obtained from Solar system tests.Comment: 28 pages, 20 figure
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