Particles in the superworldline and BRST

Eugenia Boffo

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Displaying similar documents to “Particles in the superworldline and BRST”

$L^{2}$ -cohomology

J. Eichhorn (1986)

Banach Center Publications

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Batalin-Vilkovisky algebra structures on Hochschild cohomology

Luc Menichi (2009)

Bulletin de la Société Mathématique de France

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Let $M$ be any compact simply-connected oriented $d$ -dimensional smooth manifold and let $𝔽$ be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of $M$ , $H H^{*} (S^{*} (M), S^{*} (M))$ , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on $M$ , $H_{* + d} (L M)$ introduced by Chas and Sullivan. We also show that the negative cyclic...

A note on the cohomology ring of the oriented Grassmann manifolds ${\tilde{G}}_{n, 4}$

Tomáš Rusin (2019)

Archivum Mathematicum

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We use known results on the characteristic rank of the canonical $4$ –plane bundle over the oriented Grassmann manifold ${\tilde{G}}_{n, 4}$ to compute the generators of the $ℤ_{2}$ –cohomology groups $H^{j} ({\tilde{G}}_{n, 4})$ for $n = 8, 9, 10, 11$ . Drawing from the similarities of these examples with the general description of the cohomology rings of ${\tilde{G}}_{n, 3}$ we conjecture some predictions.

Quantum Singularity Theory for $A_{(r - 1)}$ and $r$ -Spin Theory

Huijun Fan, Tyler Jarvis, Yongbin Ruan (2011)

Annales de l’institut Fourier

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We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the $r$ -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity $W$ of type $A$ our construction of the stack of $W$ -curves is canonically isomorphic to the stack of $r$ -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an $r$ -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine...

Chen–Ruan Cohomology of $ℳ_{1, n}$ and ${\bar{ℳ}}_{1, n}$

Nicola Pagani (2013)

Annales de l’institut Fourier

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In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable $n$ -pointed curves of genus $1$ . In the first part of the paper we study and describe stack theoretically the twisted sectors of $ℳ_{1, n}$ and ${\bar{ℳ}}_{1, n}$ . In the second part, we study the orbifold intersection theory of ${\bar{ℳ}}_{1, n}$ . We suggest a definition for an orbifold tautological ring in genus $1$ , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.

$1$ -cocycles on the group of contactomorphisms on the supercircle $S^{1 | 3}$ generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

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The relative cohomology $H_{diff}^{1} (𝕂 (1 | 3), 𝔬𝔰𝔭 (2, 3); 𝒟_{λ, μ} (S^{1 | 3}))$ of the contact Lie superalgebra $𝕂 (1 | 3)$ with coefficients in the space of differential operators $𝒟_{λ, μ} (S^{1 | 3})$ acting on tensor densities on $S^{1 | 3}$ , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating $1$ -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative $1$ -cocycle $s (X_{f}) = D_{1} D_{2} D_{3} (f) α_{3}^{1 / 2}$ , $X_{f} \in 𝕂 (1 | 3)$ which is invariant with respect to the conformal subsuperalgebra $𝔬𝔰𝔭 (2, 3)$ of $𝕂 (1 | 3)$ . In this work we study the supergroup case. We give an explicit construction of $1$ -cocycles...

Stability and semiclassics in self-generated fields

László Erdős, Soren Fournais, Jan Philip Solovej (2013)

Journal of the European Mathematical Society

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We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$ . The total energy includes the field energy $β \int B^{2}$ and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter $β$ tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and...

Overconvergent de Rham-Witt cohomology

Christopher Davis, Andreas Langer, Thomas Zink (2011)

Annales scientifiques de l'École Normale Supérieure

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The goal of this work is to construct, for a smooth variety $X$ over a perfect field k of finite characteristic $p > 0$ , an overconvergent de Rham-Witt complex $W^{†} Ω_{X / k}$ as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in $X$ , is a complex of étale sheaves and a differential graded algebra over the ring $W^{†} (𝒪_{X})$ of overconvergent Witt-vectors. If $X$ is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

On $1$ -cocycles induced by a positive definite function on a locally compact abelian group

Jordan Franks, Alain Valette (2014)

Annales mathématiques Blaise Pascal

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For $ϕ$ a normalized positive definite function on a locally compact abelian group $G$ , let $π_{ϕ}$ be the unitary representation associated to $ϕ$ by the GNS construction. We give necessary and sufficient conditions for the vanishing of 1-cohomology $H^{1} (G, π_{ϕ})$ and reduced 1-cohomology ${\bar{H}}^{1} (G, π_{ϕ})$ . For example, ${\bar{H}}^{1} (G, π_{ϕ}) = 0$ if and only if either $Hom (G, ℂ) = 0$ or $μ_{ϕ} (1_{G}) = 0$ , where $1_{G}$ is the trivial character of $G$ and $μ_{ϕ}$ is the probability measure on the Pontryagin dual $\hat{G}$ associated to $ϕ$ by Bochner’s Theorem. This streamlines an argument of Guichardet...

Duality in $N = 2$ Susy $S U (2)$ Yang-Mills Theory : A Pedagogical Introduction to the Work of Seiberg and Witten

Adel Bilal (1997)

Recherche Coopérative sur Programme n°25

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A Deformed Quon Algebra

Hery Randriamaro (2019)

Communications in Mathematics

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The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators $a_{i, k}$ , $(i, k) \in ℕ^{*} \times [m]$ , on an infinite dimensional vector space satisfying...

Invariants, torsion indices and oriented cohomology of complete flags

Baptiste Calmès, Viktor Petrov, Kirill Zainoulline (2013)

Annales scientifiques de l'École Normale Supérieure

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Let $G$ be a split semisimple linear algebraic group over a field and let $T$ be a split maximal torus of $G$ . Let $𝗁$ be an oriented cohomology (algebraic cobordism, connective $K$ -theory, Chow groups, Grothendieck’s $K_{0}$ , etc.) with formal group law $F$ . We construct a ring from $F$ and the characters of $T$ , that we call a formal group ring, and we define a characteristic ring morphism $c$ from this formal group ring to $𝗁 (G / B)$ where $G / B$ is the variety of Borel subgroups of $G$ . Our main result says that when the...

Poincaré inequalities and rigidity for actions on Banach spaces

Piotr Nowak (2015)

Journal of the European Mathematical Society

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The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present a condition implying that every affine isometric action of a given group $G$ on a reflexive Banach space $X$ has a fixed point. This last property is a strong version of Kazhdan’s property (T) and is equivalent to the fact that $H^{1} (G, π) = 0$ for every isometric representation $π$ of $G$ on $X$ . The condition is expressed in terms of $p$ -Poincaré constants and we...

Matlis dual of local cohomology modules

Batoul Naal, Kazem Khashyarmanesh (2020)

Czechoslovak Mathematical Journal

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Let $(R, 𝔪)$ be a commutative Noetherian local ring, $𝔞$ be an ideal of $R$ and $M$ a finitely generated $R$ -module such that $𝔞 M \neq M$ and $cd (𝔞, M) - grade (𝔞, M) \leq 1$ , where $cd (𝔞, M)$ is the cohomological dimension of $M$ with respect to $𝔞$ and $grade (𝔞, M)$ is the $M$ -grade of $𝔞$ . Let $D (-) : = {Hom}_{R} (-, E)$ be the Matlis dual functor, where $E : = E (R / 𝔪)$ is the injective hull of the residue field $R / 𝔪$ . We show that there exists the following long exact sequence $\begin{matrix} 0 ⟶ & H_{𝔞}^{n - 2} (D (H_{𝔞}^{n - 1} (M))) ⟶ H_{𝔞}^{n} (D (H_{𝔞}^{n} (M))) ⟶ D (M) \\ ⟶ & H_{𝔞}^{n - 1} (D (H_{𝔞}^{n - 1} (M))) ⟶ H_{𝔞}^{n + 1} (D (H_{𝔞}^{n} (M))) \\ ⟶ & H_{𝔞}^{n} (D (H_{(x_{1}, ..., x_{n - 1})}^{n - 1} (M))) ⟶ H_{𝔞}^{n} (D (H_{(}^{n - 1} M))) ⟶ ..., \end{matrix}$ where $n : = cd (𝔞, M)$ is a non-negative integer, $x_{1}, ..., x_{n - 1}$ is a regular sequence in $𝔞$ on $M$ and, for an $R$ -module $L$ , $H_{𝔞}^{i} (L)$ is the $i$ th local cohomology module...

Bounded cohomology and isometry groups of hyperbolic spaces

Ursula Hamenstädt (2008)

Journal of the European Mathematical Society

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Let $X$ be an arbitrary hyperbolic geodesic metric space and let $Γ$ be a countable subgroup of the isometry group $Iso (X)$ of $X$ . We show that if $Γ$ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups $H_{b}^{2} (Γ, ℝ)$ , $H_{b}^{2} (Γ, ℓ^{p} (Γ))$ $(1 < p < \infty)$ are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct...

Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

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The class of loop spaces of which the mod $p$ cohomology is Noetherian is much larger than the class of $p$ -compact groups (for which the mod $p$ cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as $ℂ P^{\infty}$ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space $B X$ of such an object and prove it is as small as expected, that is, comparable to that of $B ℂ P^{\infty}$ . We also show that $B$ X differs basically from the classifying space of a $p$ -compact...