共查询到20条相似文献,搜索用时 312 毫秒
1.
Yung-Ning Peng 《Letters in Mathematical Physics》2014,104(1):89-102
Let ${Y_{m|n}^{\ell}}$ be the super Yangian of general linear Lie superalgebra for ${\mathfrak{gl}_{m|n}}$ . Let ${e \in \mathfrak{gl}_{m\ell|n\ell}}$ be a “rectangular” nilpotent element and ${\mathcal{W}_e}$ be the finite W-superalgebra associated to e. We show that ${Y_{m|n}^{\ell}}$ is isomorphic to ${\mathcal{W}_e}$ . 相似文献
2.
Pieter Naaijkens 《Letters in Mathematical Physics》2012,101(3):341-354
We prove that Haag duality holds for cones in the toric code model. That is, for a cone ??, the algebra ${\mathcal{R}_{\Lambda}}$ of observables localized in ?? and the algebra ${\mathcal{R}_{\Lambda^c}}$ of observables localized in the complement ?? c generate each other??s commutant as von Neumann algebras. Moreover, we show that the distal split property holds: if ${\Lambda_1 \subset \Lambda_2}$ are two cones whose boundaries are well separated, there is a Type I factor ${\mathcal{N}}$ such that ${\mathcal{R}_{\Lambda_1} \subset \mathcal{N} \subset \mathcal{R}_{\Lambda_2}}$ . We demonstrate this by explicitly constructing ${\mathcal{N}}$ . 相似文献
3.
Tom Cooney Marius Junge Miguel Navascués David Pérez-García Ignacio Villanueva 《Communications in Mathematical Physics》2013,319(2):501-513
We study the entropy flux in the stationary state of a finite one-dimensional sample ${\mathcal{S}}$ connected at its left and right ends to two infinitely extended reservoirs ${\mathcal{R}_{l/r}}$ at distinct (inverse) temperatures ${\beta_{l/r}}$ and chemical potentials ${\mu_{l/r}}$ . The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator ${h_{\mathcal{S}, L}= - \Delta + v}$ . The Landauer-Büttiker formula expresses the steady state entropy flux in the coupled system ${\mathcal{R}_l + \mathcal{S} + \mathcal{R}_r}$ in terms of scattering data. We study the behaviour of this steady state entropy flux in the limit ${L \to \infty}$ and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrödinger operator ${h_\mathcal{S}}$ . 相似文献
4.
Sebastiano Carpi Yasuyuki Kawahigashi Roberto Longo 《Communications in Mathematical Physics》2013,322(1):149-166
Given a conformal QFT local net of von Neumann algebras ${\mathcal {B}_2}$ on the two-dimensional Minkowski spacetime with irreducible subnet ${\mathcal {A} \otimes \mathcal {A}}$ , where ${\mathcal {A}}$ is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to ${\mathcal {B}_2}$ : we provide a procedure to construct a Boundary CFT net ${\mathcal {B}}$ of von Neumann algebras on the half-plane x > 0, associated with ${\mathcal {A}}$ , and locally isomorphic to ${\mathcal {B}_2}$ . All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of ${\mathcal {B}_2}$ to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S 1. 相似文献
5.
Let $\mathcal{B}(\mathcal{H})$ be the set of all bounded linear operators on the separable Hilbert space $\mathcal{H}$ . A (generalized) quantum operation is a bounded linear operator defined on $\mathcal{B}(\mathcal{H})$ , which has the form $\varPhi_{\mathcal{A}}(X)=\sum_{i=1}^{\infty}A_{i}XA_{i}^{*}$ , where $A_{i}\in\mathcal{B}(\mathcal{H})$ (i=1,2,…) satisfy $\sum_{i=1}^{\infty}A_{i}A_{i}^{*}\leq \nobreak I$ in the strong operator topology. In this paper, we establish the relationship between the (generalized) quantum operation $\varPhi_{\mathcal{A}}$ and its dual $\varPhi_{\mathcal {A}}^{\dag}$ with respect to the set of fixed points and the noiseless subspace. In particular, we also partially characterize the extreme points of the set of all (generalized) quantum operations and give some equivalent conditions for the correctable quantum channel. 相似文献
6.
We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras ${\mathcal A_V}$ on the Minkowski half-plane M + starting with a local conformal net ${\mathcal A}$ of von Neumann algebras on ${\mathbb R}$ and an element V of a unitary semigroup ${\mathcal E(\mathcal A)}$ associated with ${\mathcal A}$ . The case V?=?1 reduces to the net ${\mathcal A_+}$ considered by Rehren and one of the authors; if the vacuum character of ${\mathcal A}$ is summable, ${\mathcal A_V}$ is locally isomorphic to ${\mathcal A_+}$ . We discuss the structure of the semigroup ${\mathcal E(\mathcal A)}$ . By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to ${\mathcal E(\mathcal A^{(0)})}$ with ${\mathcal A^{(0)}}$ the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mack-Todorov extension of ${\mathcal A^{(0)}}$ . A further family of models comes from the Ising model. 相似文献
7.
Jorge Antezana Gabriel Larotonda Alejandro Varela 《Communications in Mathematical Physics》2014,328(2):481-497
Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold. 相似文献
8.
9.
Paul Johnson 《Communications in Mathematical Physics》2014,327(2):333-386
We extend Okounkov and Pandharipande’s work on the equivariant Gromov–Witten theory of ${\mathbb{P}^1}$ to a class of stacky curves ${\mathcal{X}}$ . Our main result uses virtual localization and the orbifold ELSV formula to express the tau function ${\tau_\mathcal{X}}$ as a vacuum expectation on a Fock space. As corollaries, we prove the decomposition conjecture for these ${\mathcal{X}}$ , and prove that ${\tau_\mathcal{X}}$ satisfies a version of the 2-Toda hierarchy. Coupled with degeneration techniques, the result should lead to treatment of general orbifold curves. 相似文献
10.
Sergey Neshveyev 《Letters in Mathematical Physics》2014,104(3):361-371
Assume ${\mathcal{A}}$ is a Fréchet algebra equipped with a smooth isometric action of a vector group V, and consider Rieffel’s deformation ${\mathcal{A}_J}$ of ${\mathcal{A}}$ . We construct an explicit isomorphism between the smooth crossed products ${V\ltimes\mathcal{A}_J}$ and ${V\ltimes\mathcal{A}}$ . When combined with the Elliott–Natsume–Nest isomorphism, this immediately implies that the periodic cyclic cohomology is invariant under deformation. Specializing to the case of smooth subalgebras of C*-algebras, we also get a simple proof of equivalence of Rieffel’s and Kasprzak’s approaches to deformation. 相似文献
11.
Richard Kenyon 《Communications in Mathematical Physics》2014,326(2):477-497
The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph ${\mathcal{G}}$ is a union of two dimer covers of ${\mathcal{G}}$ . We introduce quaternion weights in the dimer model and show how they can be used to study the homotopy classes (relative to a fixed set of faces) of loops in the double dimer model on a planar graph. As an application we prove that, in the scaling limit of the “uniform” double-dimer model on ${\mathbb{Z}^2}$ (or on any other bipartite planar graph conformally approximating ${\mathbb{C}}$ ), the loops are conformally invariant. As other applications we compute the exact distribution of the number of topologically nontrivial loops in the double-dimer model on a cylinder and the expected number of loops surrounding two faces of a planar graph. 相似文献
12.
Giulio Bonelli Kazunobu Maruyoshi Alessandro Tanzini 《Letters in Mathematical Physics》2012,101(1):103-124
We present a relation between ${\mathcal{N}=2}$ quiver gauge theories on the ALE space ${\mathcal{O}_{\mathbb{P}^1}(-2)}$ and correlators of ${\mathcal{N}=1}$ super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the ${\mathcal{N}=2^*}$ instanton partition function is given by the product of the character of ${\widehat{SU}(2)_2}$ times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions. 相似文献
13.
Tudor Dimofte Davide Gaiotto Sergei Gukov 《Communications in Mathematical Physics》2014,325(2):367-419
We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional ${\mathcal{N} = 2}$ gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that ${S^{3}_{b}}$ partition functions of two mirror 3d ${\mathcal{N} = 2}$ gauge theories are equal. Three-dimensional ${\mathcal{N} = 2}$ field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional ${\mathcal{N} = 2}$ SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing. 相似文献
14.
Dmitry Roytenberg 《Letters in Mathematical Physics》2009,90(1-3):311-351
We introduce a new type of algebra, the Courant–Dorfman algebra. These are to Courant algebroids what Lie–Rinehart algebras are to Lie algebroids, or Poisson algebras to Poisson manifolds. We work with arbitrary rings and modules, without any regularity, finiteness or non-degeneracy assumptions. To each Courant–Dorfman algebra ${(\mathcal{R}, \mathcal{E})}$ we associate a differential graded algebra ${\mathcal{C}(\mathcal{E}, \mathcal{R})}$ in a functorial way by means of explicit formulas. We describe two canonical filtrations on ${\mathcal{C}(\mathcal{E}, \mathcal{R})}$ , and derive an analogue of the Cartan relations for derivations of ${\mathcal{C}(\mathcal{E}, \mathcal{R})}$ ; we classify central extensions of ${\mathcal{E}}$ in terms of ${H^2(\mathcal{E}, \mathcal{R})}$ and study the canonical cocycle ${\Theta \in \mathcal{C}^3(\mathcal{E}, \mathcal{R})}$ whose class ${[\Theta]}$ obstructs re-scalings of the Courant–Dorfman structure. In the nondegenerate case, we also explicitly describe the Poisson bracket on ${\mathcal{C}(\mathcal{E}, \mathcal{R})}$ ; for Courant–Dorfman algebras associated to Courant algebroids over finite-dimensional smooth manifolds, we prove that the Poisson dg algebra ${\mathcal{C}(\mathcal{E}, \mathcal{R})}$ is isomorphic to the one constructed in Roytenberg (On the structure of graded symplectic supermanifolds and Courant algebroids. American Mathematical Society, Providence, 2002) using graded manifolds. 相似文献
15.
M. D. Pollock 《Foundations of Physics》2014,44(4):368-388
The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$ . 相似文献
16.
The Lie–Rinehart algebra of a (connected) manifold ${\mathcal {M}}$ , defined by the Lie structure of the vector fields, their action and their module structure over ${C^\infty({\mathcal {M}})}$ , is a common, diffeomorphism invariant, algebra for both classical and quantum mechanics. Its (noncommutative) Poisson universal enveloping algebra ${\Lambda_{R}({\mathcal {M}})}$ , with the Lie–Rinehart product identified with the symmetric product, contains a central variable (a central sequence for non-compact ${{\mathcal {M}}}$ ) ${Z}$ which relates the commutators to the Lie products. Classical and quantum mechanics are its only factorial realizations, corresponding to Z = i z, z = 0 and ${z = \hbar}$ , respectively; canonical quantization uniquely follows from such a general geometrical structure. For ${z =\hbar \neq 0}$ , the regular factorial Hilbert space representations of ${\Lambda_{R}({\mathcal{M}})}$ describe quantum mechanics on ${{\mathcal {M}}}$ . For z = 0, if Diff( ${{\mathcal {M}}}$ ) is unitarily implemented, they are unitarily equivalent, up to multiplicity, to the representation defined by classical mechanics on ${{\mathcal {M}}}$ . 相似文献
17.
The Sklyanin algebra ${\mathcal{S}_{\eta}}$ has a well-known family of infinite-dimensional representations ${\mathcal{D}(\mu), {\mu}\,{\in}\,\mathbb{C}^{\ast}}$ , in terms of difference operators with shift η acting on even meromorphic functions. We show that for generic η the coefficients of these operators have solely simple poles, with linear residue relations depending on their locations. More generally, we obtain explicit necessary and sufficient conditions on a difference operator for it to belong to ${\mathcal{D}(\mu)}$ . By definition, the even part of ${\mathcal{D}(\mu)}$ is generated by twofold products of the Sklyanin generators. We prove that any sum of the latter products yields a difference operator of van Diejen type. We also obtain kernel identities for the Sklyanin generators. They give rise to order-reversing involutive automorphisms of ${\mathcal{D}(\mu)}$ , and are shown to entail previously known kernel identities for the van Diejen operators. Moreover, for special μ they yield novel finite-dimensional representations of ${\mathcal{S}_{\eta}}$ . 相似文献
18.
Anton Gerasimov Dimitri Lebedev Sergey Oblezin 《Communications in Mathematical Physics》2010,294(1):121-143
A representation of a specialization of a q-deformed class one lattice ${\mathfrak{gl}_{\ell+1}}$ -Whittaker function in terms of cohomology groups of line bundles on the space ${\mathcal{QM}_d(\mathbb{P}^{\ell})}$ of quasi-maps ${\mathbb{P}^1 \to \mathbb{P}^{\ell}}$ of degree d is proposed. For ? = 1, this provides an interpretation of the non-specialized q-deformed ${\mathfrak{gl}_{2}}$ -Whittaker function in terms of ${\mathcal{QM}_d(\mathbb{P}^1)}$ . In particular the (q-version of the) Mellin-Barnes representation of the ${\mathfrak{gl}_2}$ -Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed ${\mathfrak{gl}_2}$ -Toda chain is also discussed. 相似文献
19.
In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses. 相似文献
20.
K. Muralidhar 《Foundations of Physics》2014,44(3):266-295
Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. 相似文献