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Alexander Schmidt

Publications and source records attributed to Alexander Schmidt.

At least 55 records · Page 3Linked to original sources
arXiv2011

Center clusters in the Yang-Mills vacuum

Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory at finite temperature are analyzed. We show that spatial clusters can be identified where the local Polyakov loops have values close to the same center element. For a suitable definition of these clusters the deconfinement transition can be characterized by the onset of percolation in one of the center sectors. The analysis is repeated for different resolution scales of the lattice and we argue that the center clusters have a continuum limit.

hep-lat↗
arXiv2010

Coherent center domains from local Polyakov loops

We analyze properties of local Polyakov loops using quenched as well as dynamical SU(3) gauge configurations for a wide range of temperatures. It is demonstrated that for both, the confined and the deconfined regime, the local Polyakov loop prefers phase values near the center elements 1, exp(i 2 pi/3), exp(-i 2 pi/3). We divide the lattice sites into three sectors according to these phases and show that the sectors give rise to the formation of clusters. For a suitable definition of these clusters we find that in the quenched case deconfinement manifests itself as the onset of percolation of the clusters. A possible continuum limit of the center clusters is discussed.

hep-lat↗
arXiv2009

On different notions of tameness in arithmetic geometry

The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these definitions are essentially equivalent. Furthermore, we prove finiteness theorems for the tame fundamental groups of arithmetic schemes.

math.AG↗
arXiv2009

Covering data and higher dimensional global class field theory

For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism ρ_X: C_X --> π_1^\ab(X), which is surjective and whose kernel is the connected component of the identity. The (topological) group C_X is explicitly given and built solely out of data attached to points and curves on X. A similar but weaker statement holds for smooth varieties over finite fields. Our results are based on earlier work of G. Wiesend.

math.NT↗
arXiv2009

Über Pro-p-Fundamentalgruppen markierter arithmetischer Kurven

Let k be a global field, p an odd prime number different from char(k) and S, T disjoint, finite sets of primes of k. Let G_S^T(k)(p)=Gal(k_S^T(p)|k) be the Galois group of the maximal p-extension of k which is unramified outside S and completely split at T. We prove the existence of a finite set of primes S_0, which can be chosen disjoint from any given set M of Dirichlet density zero, such that the cohomology of G_{S\cup S_0}^T(k)(p) coincides with the etale cohomology of the associated marked arithmetic curve. In particular, cd G_{S\cup S_0}^T(k)(p)=2. Furthermore, we can choose S_0 in such a way that k_{S\cup S_0}^T(p) realizes the maximal p-extension k_\p(p) of the local field k_\p for all \p\in S\cup S_0, the cup-product H^1(G_{S\cup S_0}^T(k)(p),\F_p) \otimes H^1(G_{S\cup S_0}^T(k)(p),\F_p) --> H^2(G_{S\cup S_0}^T(k)(p),\F_p) is surjective and the decomposition groups of the primes in S establish a free product inside G_{S\cup S_0}^T(k)(p). This generalizes previous work of the author where similar results were shown in the case T=\emptyset under the restrictive assumption p\nmid Cl(k) and ζ_p\notin k.

math.NT↗
arXiv2009

On pro-p fundamental groups of marked arithmetic curves

Let k be a global field, p an odd prime number different from char(k) and S, T disjoint, finite sets of primes of k. Let G_S^T(k)(p)=Gal(k_S^T(p)|k) be the Galois group of the maximal p-extension of k which is unramified outside S and completely split at T. We prove the existence of a finite set of primes S_0, which can be chosen disjoint from any given set M of Dirichlet density zero, such that the cohomology of G_{S\cup S_0}^T(k)(p) coincides with the etale cohomology of the associated marked arithmetic curve. In particular, cd G_{S\cup S_0}^T(k)(p)=2. Furthermore, we can choose S_0 in such a way that k_{S\cup S_0}^T(p) realizes the maximal p-extension k_\p(p) of the local field k_\p for all \p\in S\cup S_0, the cup-product H^1(G_{S\cup S_0}^T(k)(p),\F_p) \otimes H^1(G_{S\cup S_0}^T(k)(p),\F_p) --> H^2(G_{S\cup S_0}^T(k)(p),\F_p) is surjective and the decomposition groups of the primes in S establish a free product inside G_{S\cup S_0}^T(k)(p). This generalizes previous work of the author where similar results were shown in the case T=\emptyset under the restrictive assumption p\nmid Cl(k) and ζ_p\notin k.

math.NT↗
arXiv2008

Pro-p groups of positive deficiency

Let Γbe a finitely presentable pro-p group with a nontrivial finitely generated closed normal subgroup N of infinite index. Then def(Γ)\leq 1, and if def(Γ)=1 then Γis a pro-p duality group of dimension 2, N is a free pro-p group and Γ/N is virtually free. In particular, if the centre of Γis nontrivial and def(Γ)\geq 1, then def(Γ)=1, cd G \leq 2 and Γis virtually a direct product F \times Z_p, with F a finitely generated free pro-p group.

math.GR↗
arXiv2008

Extensions of profinite duality groups

We show that the class of profinite duality groups is closed under group extensions provided that the kernel satisfies some finiteness condition. This extends earlier results of Pletch and of Wingberg.

math.GR↗
arXiv2008

On the K(π,1)-property for rings of integers in the mixed case

We investigate the Galois group G_S(p) of the maximal p-extension unramified outside a finite set S of primes of a number field in the (mixed) case, when there are primes dividing p inside and outside S. We show that the cohomology of G_S(p) is "often" isomorphic to the etale cohomology of the scheme Spec(O_k S), in particular, G_S(p) is of cohomological dimension 2 then. We deduce this from the results in our previous paper "Rings of integers of type K(π,1)" (arXiv:0705.3372), which mainly dealt with the tame case.

math.NT↗
arXiv2007

Rings of integers of type $K(π,1)$

We investigate the Galois group $G_S(p)$ of the maximal $p$-extension unramified outside a finite $S$ of primes of a number field in the (tame) case, when no prime dividing $p$ is in $S$. We show that the cohomology of $G_S(p)$ is 'often' isomorphic to the etale cohomology of the scheme $\Spec(Ø_k \sm S)$, in particular, $G_S(p)$ is of cohomological dimension~2 then.

math.NT↗
arXiv2007

Discovery Potential for the SM Higgs Boson in the Inclusive Search Channels

This paper gives an overview of the potential to discover a Standard Model Higgs Boson in the inclusive search channels at the ATLAS and CMS experiments at the LHC. The most important decay modes, $H \to γγ$, $H \to WW \to llνν$ and $H \to ZZ \to 4l$ are described and a summary of recently published analyses using realistic detector simulations is presented.

hep-ex↗
arXiv2007

q-Deformed Superalgebras

The article deals with q-analogs of the three- and four-dimensional Euclidean superalgebra and the Poincare superalgebra.

hep-th↗
arXiv2007

Singular Homology of Arithmetic Schemes

We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular homology in degree zero and the abelianized modified tame fundamental group.

math.NT↗
arXiv2007

Spinor calculus for q-deformed quantum spaces I

The article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and higher-dimensional quantum spaces like the q-deformed Euclidean space in four dimensions or the q-deformed Minkowski space is outlined. These considerations are continued by introducing q-analogs of the Pauli matrices. Their main properties are discussed in detail and numerous relations that could prove useful in physical applications are presented. In this respect, q-deformed versions of the important Fierz identities are written down.

hep-th↗
arXiv2007

Spinor calculus for q-deformed quantum spaces II

This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. The Clifford algebras corresponding to these quantum spaces are treated. Especially, their commutation relations and their Hopf structures are written down. Bases of the four-dimensional Clifford algebras are constructed and their properties are discussed. Matrix representations of the Clifford algebras lead to q-deformed Dirac-matrices for the four-dimensional quantum spaces. Moreover, q-analogs of the four-dimensional spin matrices are presented. A very complete set of trace relations and rearrangement formulae concerning spin and Dirac-matrices is given. Dirac spinors together with their bilinear covariants are defined. Their behavior under q-deformed Lorentz transformation is discussed in detail.

hep-th↗
arXiv2006

Grassmann variables on quantum spaces

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused together.

hep-th↗
arXiv2006

Circular sets of prime numbers and p-extension of the rationals

Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group G_S(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that G_S(Q)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension Q_S(p)/Q and we relate the cohomology of G_S(Q)(p) to the etale cohomology of the scheme Spec(Z)-S. Finally, we calculate the dualizing module.

math.NT↗
arXiv2005

The PAX Toolkit and its Applications at Tevatron and LHC

At the CHEP03 conference we launched the Physics Analysis eXpert (PAX), a C++ toolkit released for the use in advanced high energy physics (HEP) analyses. This toolkit allows to define a level of abstraction beyond detector reconstruction by providing a general, persistent container model for HEP events. Physics objects such as particles, vertices and collisions can easily be stored, accessed and manipulated. Bookkeeping of relations between these objects (like decay trees, vertex and collision separation, etc.) including deep copies is fully provided by the relation management. Event container and associated objects represent a uniform interface for algorithms and facilitate the parallel development and evaluation of different physics interpretations of individual events. So-called analysis factories, which actively identify and distinguish different physics processes and study systematic uncertainties, can easily be realized with the PAX toolkit. PAX is officially released to experiments at Tevatron and LHC. Being explored by a growing user community, it is applied in a number of complex physics analyses, two of which are presented here. We report the successful application in studies of t-tbar production at the Tevatron and Higgs searches in the channel t-tbar-Higgs at the LHC and give a short outlook on further developments.

physics.data-an↗