715 research outputs found
Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane
We consider bosons on Euclidean R^4 that are minimally coupled to an external
Yang-Mills field. We compute the logarithmically divergent part of the cut-off
regularized quantum effective action of this system. We confirm the known
result that this term is proportional to the Yang-Mills action.
We use pseudodifferential operator methods throughout to prepare the ground
for a generalization of our calculation to the noncommutative four-dimensional
Moyal plane (also known as noncommutative flat space). We also include a
detailed comparison of our cut-off regularization to heat kernel techniques.
In the case of the noncommutative space, we complement the usual technique of
asymptotic expansion in the momentum variable with operator theoretic arguments
in order to keep separated quantum from noncommutativity effects. We show that
the result from the commutative space R^4 still holds if one replaces all
pointwise products by the noncommutative Moyal product.Comment: 37 pages, v2 contains an improved treatment of the theta function in
Appendix A.
Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic pseudo-differential operators
We obtain a complete asymptotic expansion of the integrated density of states
of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs to
a wide class of almost-periodic self-adjoint pseudo-differential operators of
order less than 2w. In particular, we obtain such an expansion for magnetic
Schr\"odinger operators with either smooth periodic or generic almost-periodic
coefficients.Comment: 47 pages. arXiv admin note: text overlap with arXiv:1004.293
Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold
We consider the index problem for a wide class of nonlocal elliptic operators
on a smooth closed manifold, namely differential operators with shifts induced
by the action of an isometric diffeomorphism. The key to the solution is the
method of uniformization: We assign to the nonlocal problem a
pseudodifferential operator with the same index, acting in sections of an
infinite-dimensional vector bundle on a compact manifold. We then determine the
index in terms of topological invariants of the symbol, using the Atiyah-Singer
index theorem.Comment: 16 pages, no figure
Innovative solutions to protect scientific and technological equipment from vibrations
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Conormal distributions in the Shubin calculus of pseudodifferential operators
We characterize the Schwartz kernels of pseudodifferential operators of
Shubin type by means of an FBI transform. Based on this we introduce as a
generalization a new class of tempered distributions called Shubin conormal
distributions. We study their transformation behavior, normal forms and
microlocal properties.Comment: 23 page
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Fin ray patterns at the fin-to-limb transition
The fin-to-limb transition was marked by the origin of digits and the loss of dermal fin rays. Paleontological research into this transformation has focused on the evolution of the endoskeleton, with little attention paid to fin ray structure and function. To address this knowledge gap, we study the dermal rays of the pectoral fins of 3 key tetrapodomorph taxa—Sauripterus taylori (Rhizodontida), Eusthenopteron foordi (Tristichopteridae), and Tiktaalik roseae (Elpistostegalia)—using computed tomography. These data show several trends in the lineage leading to digited forms, including the consolidation of fin rays (e.g., reduced segmentation and branching), reduction of the fin web, and unexpectedly, the evolution of asymmetry between dorsal and ventral hemitrichia. In Eusthenopteron, dorsal rays cover the preaxial endoskeleton slightly more than ventral rays. In Tiktaalik, dorsal rays fully cover the third and fourth mesomeres, while ventral rays are restricted distal to these elements, suggesting the presence of ventralized musculature at the fin tip analogous to a fleshy “palm.” Asymmetry is also observed in cross-sectional areas of dorsal and ventral rays. Eusthenopteron dorsal rays are slightly larger than ventral rays; by contrast, Tiktaalik dorsal rays can be several times larger than ventral rays, and degree of asymmetry appears to be greater at larger sizes. Analysis of extant osteichthyans suggests that cross-sectional asymmetry in the dermal rays of paired fins is plesiomorphic to crown group osteichthyans. The evolution of dermal rays in crownward stem tetrapods reflects adaptation for a fin-supported elevated posture and resistance to substrate-based loading prior to the origin of digits
The Gabor wave front set of compactly supported distributions
We show that the Gabor wave front set of a compactly supported distribution
equals zero times the projection on the second variable of the classical wave
front set
Analytic and Reidemeister torsion for representations in finite type Hilbert modules
For a closed Riemannian manifold we extend the definition of analytic and
Reidemeister torsion associated to an orthogonal representation of fundamental
group on a Hilbert module of finite type over a finite von Neumann algebra. If
the representation is of determinant class we prove, generalizing the
Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal.
In particular, this proves the conjecture that for closed Riemannian manifolds
with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister
torsions are equal.Comment: 78 pages, AMSTe
Comparative energies of Zn(II) cation localization as a function of the distance between two forming cation position aluminium ions in high-silica zeolites
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