2,972 research outputs found
Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the -Function Potential in 1-dimensional Relativistic Quantum Mechanics
We consider the Schr\"odinger equation for a relativistic point particle in
an external 1-dimensional -function potential. Using dimensional
regularization, we investigate both bound and scattering states, and we obtain
results that are consistent with the abstract mathematical theory of
self-adjoint extensions of the pseudo-differential operator . Interestingly, this relatively simple system is asymptotically free. In
the massless limit, it undergoes dimensional transmutation and it possesses an
infra-red conformal fixed point. Thus it can be used to illustrate non-trivial
concepts of quantum field theory in the simpler framework of relativistic
quantum mechanics
Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity
The non-relativistic hydrogen atom enjoys an accidental symmetry,
that enlarges the rotational symmetry, by extending the angular
momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom
the accidental symmetry is partially lifted. Due to the Johnson-Lippmann
operator, which commutes with the Dirac Hamiltonian, some degeneracy remains.
When the non-relativistic hydrogen atom is put in a spherical cavity of radius
with perfectly reflecting Robin boundary conditions, characterized by a
self-adjoint extension parameter , in general the accidental
symmetry is lifted. However, for (where is the Bohr
radius and is the orbital angular momentum) some degeneracy remains when
or . In the relativistic case, we
consider the most general spherically and parity invariant boundary condition,
which is characterized by a self-adjoint extension parameter. In this case, the
remnant accidental symmetry is always lifted in a finite volume. We also
investigate the accidental symmetry in the context of the Pauli equation, which
sheds light on the proper non-relativistic treatment including spin. In that
case, again some degeneracy remains for specific values of and .Comment: 27 pages, 7 figure
Majorana Fermions in a Box
Majorana fermion dynamics may arise at the edge of Kitaev wires or
superconductors. Alternatively, it can be engineered by using trapped ions or
ultracold atoms in an optical lattice as quantum simulators. This motivates the
theoretical study of Majorana fermions confined to a finite volume, whose
boundary conditions are characterized by self-adjoint extension parameters.
While the boundary conditions for Dirac fermions in -d are characterized
by a 1-parameter family, , of self-adjoint extensions,
for Majorana fermions is restricted to . Based on this result,
we compute the frequency spectrum of Majorana fermions confined to a 1-d
interval. The boundary conditions for Dirac fermions confined to a 3-d region
of space are characterized by a 4-parameter family of self-adjoint extensions,
which is reduced to two distinct 1-parameter families for Majorana fermions. We
also consider the problems related to the quantum mechanical interpretation of
the Majorana equation as a single-particle equation. Furthermore, the equation
is related to a relativistic Schr\"odinger equation that does not suffer from
these problems.Comment: 23 pages, 2 figure
Interacting crumpled manifolds
In this article we study the effect of a delta-interaction on a polymerized
membrane of arbitrary internal dimension D. Depending on the dimensionality of
membrane and embedding space, different physical scenarios are observed. We
emphasize on the difference of polymers from membranes. For the latter,
non-trivial contributions appear at the 2-loop level. We also exploit a
``massive scheme'' inspired by calculations in fixed dimensions for scalar
field theories. Despite the fact that these calculations are only amenable
numerically, we found that in the limit of D to 2 each diagram can be evaluated
analytically. This property extends in fact to any order in perturbation
theory, allowing for a summation of all orders. This is a novel and quite
surprising result. Finally, an attempt to go beyond D=2 is presented.
Applications to the case of self-avoiding membranes are mentioned
Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case
Slowly walking technicolor models provide a mechanism for electroweak
symmetry breaking whose nonperturbative lattice investigation is rather
challenging. Here we demonstrate walking near a conformal fixed point
considering the 2-d lattice O(3) model at vacuum angle .
The essential features of walking technicolor models are shared by this toy
model and can be accurately investigated by numerical simulations. We show
results for the running coupling and the beta-function and we perform a finite
size scaling analysis of the massgap close to the conformal point.Comment: 5 pages, 4 figure
Gene expression and molecular evolution of sxtA4 in a saxitoxin producing dinoflagellate Alexandrium catenella
Copyright © 2014 Elsevier Ltd. All rights reserved. Dinoflagellates of the genus Alexandrium produce the neurotoxin saxitoxin (STX), responsible for paralytic shellfish poisoning (PSP) and accumulates in marine invertebrates. The recent identification of STX biosynthesis genes allowed us to investigate the expression of sxtA4 at different growth stages in Alexandrium catenella Group IV. We found no significant differences in expression of sxtA4, despite significant differences in STX levels at different growth stages (P < 0.023). Three reference genes were tested for normalisation: actin, cytochrome b (cob), and the large subunit ribosomal RNA (LSU rDNA). cob was most stably expressed but the combination of two reference genes, actin and cob, resulted in the best stability factor. Most genomic sequences of sxtA4 from A. catenella were in a clade that included sequences from Alexandrium fundyense Group I, however, one paralogue was not related to the others, suggesting recombination or lateral transfer. A comparison of the sxtA4 cDNA sequences with genomic DNA sequences indicated the possibility of transcript editing and the preferential transcription of certain genomic DNA loci. The results show that, in dinoflagellates, post-transcriptional mechanisms play a major role in the regulation of saxitoxin biosynthesis
Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
The functional RG for the random field and random anisotropy O(N)
sigma-models is studied to two loop. The ferromagnetic/disordered (F/D)
transition fixed point is found to next order in d=4+epsilon for N > N_c
(N_c=2.8347408 for random field, N_c=9.44121 for random anisotropy). For N <
N_c the lower critical dimension plunges below d=4: we find two fixed points,
one describing the quasi-ordered phase, the other is novel and describes the
F/D transition. The lower critical dimension can be obtained in an
(N_c-N)-expansion. The theory is also analyzed at large N and a glassy regime
is found.Comment: 4 pages, 5 figure
The nucleon spin and momentum decomposition using lattice QCD simulations
We determine within lattice QCD, the nucleon spin carried by valence and sea
quarks, and gluons. The calculation is performed using an ensemble of gauge
configurations with two degenerate light quarks with mass fixed to
approximately reproduce the physical pion mass. We find that the total angular
momentum carried by the quarks in the nucleon is and the gluon contribution is giving a total of consistent with the spin sum. For the quark intrinsic spin contribution
we obtain . All quantities are given in the scheme at
2~GeV. The quark and gluon momentum fractions are also computed and add up to
satisfying the momentum sum.Comment: Version published in PR
Two Higgs Doublet Model and Lepton Polarization in the B -> K tau+ tau- Decay
The decay width, forward-backward asymmetry and tau lepton longitudinal and
transversal polarization for the exclusive (B -> K tau^+ tau^-) decay in a two
Higgs doublet model are computed. It is shown that the forward-backward
asymmetry and longitudinal polarization of the tau lepton are very effective
tools for establishing new physics.Comment: 25 pages, 20 figures, LaTeX formatte
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