155 research outputs found
Intermolecular C-H...N and C-H...O interactions in (2S,4S,5R)-(-)-3,4-dimethyl-5-phenyl-2-(1,3-thiazol-2-yl)-1,3-oxazolidine
The title compound, CââHââNâOS, prepared from
(1R,2S)-(-)-ephedrine, contains the oxazolidine ring
in an envelope conformation, with the nitrogen atom
0.623 (2) Ă
from the plane of the other four oxazolidine ring
atoms. Intermolecular C--H...N and C--H...O interactions
generate a two-dimensional hydrogen-bonded
network, with shortest C...N and C...O distances of
3.403 (3) and 3.463 (2) Ă
, respectively
Intermolecular N-H...O and C-H...O interactions form a two-dimensional network in (2S,4S,5R)-(-)-3,4-dimethyl-5-phenyl-2-(pyrrol-2-yl)-1,3-oxazolidine
The title compound, Cââ
HââNâ0, prepared from (1R,2S)-
(-)-ephedrine, crystallizes in space group P1 with two
molecules in the asymmetric unit. The oxazolidine rings
of the two molecules adopt an envelope conformation,
with the N atom 0.609 (6) and 0.623 (6)Ă
from the
plane of the other four oxazolidine ring atoms. Intermolecular Npyrrole--H...O and Cphenyl--H...O interactions generate a two-dimensional hydrogen-bonded network with N...O and C...O distances of 3.004 (4) and
3.051 (4)Ă
, respectively, and 3.599 (5) and 3.632 (5)Ă
,
respectively, for the two independent hydrogen-bonding
systems
On One-Loop Gap Equations for the Magnetic Mass in d=3 Gauge Theory
Recently several workers have attempted determinations of the so-called
magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap
equation, using a free massive propagator as input. Self-consistency is
attained only on-shell, because the usual Feynman-graph construction is
gauge-dependent off-shell. We examine two previous studies of the pinch
technique proper self-energy, which is gauge-invariant at all momenta, using a
free propagator as input, and show that it leads to inconsistent and unphysical
result. In one case the residue of the pole has the wrong sign (necessarily
implying the presence of a tachyonic pole); in the second case the residue is
positive, but two orders of magnitude larger than the input residue, which
shows that the residue is on the verge of becoming ghostlike. This happens
because of the infrared instability of d=3 gauge theory. A possible alternative
one-loop determination via the effective action also fails. The lesson is that
gap equations must be considered at least at two-loop level.Comment: 21 pages, LaTex, 2 .eps figure
Nexus solitons in the center vortex picture of QCD
It is very plausible that confinement in QCD comes from linking of Wilson
loops to finite-thickness vortices with magnetic fluxes corresponding to the
center of the gauge group. The vortices are solitons of a gauge-invariant QCD
action representing the generation of gluon mass. There are a number of other
solitonic states of this action. We discuss here what we call nexus solitons,
in which for gauge group SU(N), up to N vortices meet a a center, or nexus,
provided that the total flux of the vortices adds to zero (mod N). There are
fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as
composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by
the flux condition; and fully non-Abelian, resembling a deformed sphaleron.
Analytic solutions are available for the quasi-Abelian case, and we discuss
variational estimates of the action of the fully non-Abelian nexus solitons in
SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge
in four dimensions). Their presence does not change the fundamentals of
confinement in the center-vortex picture, but they may lead to a modified
picture of the QCD vacuum.Comment: LateX, 24 pages, 2 .eps figure
Center vortices and confinement vs. screening
We study adjoint and fundamental Wilson loops in the center-vortex picture of
confinement, for gauge group SU(N) with general N. There are N-1 distinct
vortices, whose properties, including collective coordinates and actions, we
study. In d=2 we construct a center-vortex model by hand so that it has a
smooth large-N limit of fundamental-representation Wilson loops and find, as
expected, confinement. Extending an earlier work by the author, we construct
the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion
in powers of , where is the vortex density per unit area and M
is the vortex inverse size, and find, as expected, screening. The leading term
of the adjoint potential shows a roughly linear regime followed by string
breaking when the potential energy is about 2M. This leading potential is a
universal (N-independent at fixed fundamental string tension ) of the form
, where R is the spacelike dimension of a rectangular Wilson
loop. The linear-regime slope is not necessarily related to by Casimir
scaling. We show that in d=2 the dilute vortex model is essentially equivalent
to true d=2 QCD, but that this is not so for adjoint representations; arguments
to the contrary are based on illegal cumulant expansions which fail to
represent the necessary periodicity of the Wilson loop in the vortex flux. Most
of our arguments are expected to hold in d=3,4 also.Comment: 29 pages, LaTex, 1 figure. Minor changes; references added;
discussion of factorization sharpened. Major conclusions unchange
Speculations on Primordial Magnetic Helicity
We speculate that above or just below the electroweak phase transition
magnetic fields are generated which have a net helicity (otherwise said, a
Chern-Simons term) of order of magnitude , where is the
baryon or lepton number today. (To be more precise requires much more knowledge
of B,L-generating mechanisms than we currently have.) Electromagnetic helicity
generation is associated (indirectly) with the generation of electroweak
Chern-Simons number through B+L anomalies. This helicity, which in the early
universe is some 30 orders of magnitude greater than what would be expected
from fluctuations alone in the absence of B+L violation, should be reasonably
well-conserved through the evolution of the universe to around the times of
matter dominance and decoupling, because the early universe is an excellent
conductor. Possible consequences include early structure formation; macroscopic
manifestations of CP violation in the cosmic magnetic field (measurable at
least in principle, if not in practice); and an inverse-cascade dynamo
mechanism in which magnetic fields and helicity are unstable to transfer to
larger and larger spatial scales. We give a quasi-linear treatment of the
general-relativistic MHD inverse cascade instability, finding substantial
growth for helicity of the assumed magnitude out to scales , where is roughly the B+L to photon ratio and
is the magnetic correlation length. We also elaborate further on an
earlier proposal of the author for generation of magnetic fields above the EW
phase transition.Comment: Latex, 23 page
On The Phase Transition in D=3 Yang-Mills Chern-Simons Gauge Theory
Yang-Mills theory in three dimensions, with a Chern-Simons term of
level (an integer) added, has two dimensionful coupling constants,
and ; its possible phases depend on the size of relative to . For
, this theory approaches topological Chern-Simons theory with no
Yang-Mills term, and expectation values of multiple Wilson loops yield Jones
polynomials, as Witten has shown; it can be treated semiclassically. For ,
the theory is badly infrared singular in perturbation theory, a
non-perturbative mass and subsequent quantum solitons are generated, and Wilson
loops show an area law. We argue that there is a phase transition between these
two behaviors at a critical value of , called , with . Three lines of evidence are given: First, a gauge-invariant one-loop
calculation shows that the perturbative theory has tachyonic problems if .The theory becomes sensible only if there is an additional dynamic
source of gauge-boson mass, just as in the case. Second, we study in a
rough approximation the free energy and show that for there is a
non-trivial vacuum condensate driven by soliton entropy and driving a
gauge-boson dynamical mass , while both the condensate and vanish for . Third, we study possible quantum solitons stemming from an effective
action having both a Chern-Simons mass and a (gauge-invariant) dynamical
mass . We show that if M \gsim 0.5 m, there are finite-action quantum
sphalerons, while none survive in the classical limit , as shown earlier
by D'Hoker and Vinet. There are also quantum topological vortices smoothly
vanishing as .Comment: 36 pages, latex, two .eps and three .ps figures in a gzipped
uuencoded fil
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