
Reviews in Mathematical Physics [SJR: 1.092] [HI: 36] [0 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0129055X  ISSN (Online) 17936659 Published by World Scientific [118 journals] 
 Gauge theory approach to branes and spontaneous symmetry breaking
 Abstract: Reviews in Mathematical Physics, Volume 29, Issue 03, April 2017.
We discuss the gauge theory approach to consideration of the Nambu–Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries. The approach is generalized to describe the fundamental branes in terms of [math]dimensional worldvolume gauge and massless tensor fields consisting of the Nambu–Goldstone bosons associated with the spontaneously broken Poincaré symmetry of the [math]dimensional Minkowski space.
Citation: Reviews in Mathematical Physics
PubDate: 20170314T09:49:46Z
DOI: 10.1142/S0129055X1750009X
 Abstract: Reviews in Mathematical Physics, Volume 29, Issue 03, April 2017.
 On the 2mode and [math]photon quantum Rabi models
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
By mapping the Hamiltonians of the 2mode and 2photon Rabi models to differential operators in suitable Hilbert spaces of entire functions, we prove that the two models possess entire and normalizable wave functions in the Bargmann–Hilbert spaces only if the frequency [math] and coupling strength [math] satisfy certain constraints. This is in sharp contrast to the quantum Rabi model for which entire wave functions always exist. For model parameters fulfilling the aforesaid constraints, we determine transcendental equations whose roots give the regular energy eigenvalues of the models. Furthermore, we show that for [math], the [math]photon Rabi model does not possess wave functions which are elements of the Bargmann–Hilbert space for all nontrivial model parameters. This implies that the [math] case is not diagonalizable, unlike its RWA cousin, the [math]photon Jaynes–Cummings model which can be completely diagonalized for all [math].
Citation: Reviews in Mathematical Physics
PubDate: 20170413T01:50:47Z
DOI: 10.1142/S0129055X17500131
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
 On the equivalence of separability and extendability of quantum states
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
Motivated by the notions of [math]extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al. [Complete family of separability criteria, Phys. Rev. A 69 (2004) 022308], we introduce parallel definitions in the context of Gaussian states and using only properties of their covariance matrices, derive necessary and sufficient conditions for their complete extendability. It turns out that the complete extendability property is equivalent to the separability property of a bipartite Gaussian state. Following the proof of quantum de Finetti theorem as outlined in Hudson and Moody [Locally normal symmetric states and an analogue of de Finetti’s theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 33(4) (1975/76) 343–351], we show that separability is equivalent to complete extendability for a state in a bipartite Hilbert space where at least one of which is of dimension greater than 2. This, in particular, extends the result of Fannes, Lewis, and Verbeure [Symmetric states of composite systems, Lett. Math. Phys. 15(3) (1988) 255–260] to the case of an infinite dimensional Hilbert space whose C* algebra of all bounded operators is not separable.
Citation: Reviews in Mathematical Physics
PubDate: 20170321T03:22:41Z
DOI: 10.1142/S0129055X1750012X
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
 Klein and conformal superspaces, split algebras and spinor orbits
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
We discuss [math] Klein and Kleinconformal superspaces in [math] spacetime dimensions, realizing them in terms of their functor of points over the split composition algebra [math]. We exploit the observation that certain split forms of orthogonal groups can be realized in terms of matrix groups over split composition algebras. This leads to a natural interpretation of the sections of the spinor bundle in the critical split dimensions [math] and [math] as [math], [math] and [math], respectively. Within this approach, we also analyze the nontrivial spinor orbit stratification that is relevant in our construction since it affects the Kleinconformal superspace structure.
Citation: Reviews in Mathematical Physics
PubDate: 20170310T03:55:06Z
DOI: 10.1142/S0129055X17500118
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
 Quantum isometry groups of dual of finitely generated discrete groups and
quantum groups Abstract: Reviews in Mathematical Physics, Ahead of Print.
We study quantum isometry groups, denoted by [math], of spectral triples on [math] for a finitely generated discrete group [math] coming from the wordlength metric with respect to a symmetric generating set [math]. We first prove a few general results about [math] including: •For a group [math] with polynomial growth property, the dual of [math] has polynomial growth property provided the action of [math] on [math] has full spectrum. •[math] for any discrete abelian group [math], where [math] is a suitable metric on the dual compact abelian group [math]. We then carry out explicit computations of [math] for several classes of examples including free and direct product of cyclic groups, Baumslag–Solitar group, Coxeter groups etc. In particular, we have computed quantum isometry groups of all finitely generated abelian groups which do not have factors of the form [math] or [math] for some [math] in the direct product decomposition into cyclic subgroups.
Citation: Reviews in Mathematical Physics
PubDate: 20170217T08:40:06Z
DOI: 10.1142/S0129055X17500088
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
 Algebra of Kodaira–Spencer gravity and deformation of
Calabi–Yau manifold Abstract: Reviews in Mathematical Physics, Ahead of Print.
We study the algebraic structure of the configuration space of the Kodaira–Spencer gravity theory on a Calabi–Yau threefold. We then investigate the deformation problem of the Kodaira–Spencer gravity at the classical level using the algebraic tools obtained here.
Citation: Reviews in Mathematical Physics
PubDate: 20170217T08:40:06Z
DOI: 10.1142/S0129055X17500106
 Abstract: Reviews in Mathematical Physics, Ahead of Print.
 On weakly conformally symmetric pseudoRiemannian manifolds
 Authors: Carlo Alberto Mantica, Young Jin Suh
Abstract: Reviews in Mathematical Physics, Ahead of Print.
In this paper, we study the properties of weakly conformally symmetric pseudo Riemannian manifolds focusing particularly on the [math]dimensional Lorentzian case. First, we provide a new proof of an important result found in literature; then several new others are stated. We provide a decomposition for the conformal curvature tensor in [math]. Moreover, some important identities involving two particular covectors are stated; for example, it is proven that under certain conditions the Ricci tensor and other tensors are Weyl compatible. Topological properties involving the vanishing of the first Pontryagin form are then stated. Further, we study weakly conformally symmetric 4dimensional Lorentzian manifolds (spacetimes): it is proven that one of the previously defined covectors is null and unique up to a scaling. Moreover, it is shown that under certain conditions, the same vector is an eigenvector of the Ricci tensor and its integral curves are geodesics. Finally, it is stated that such spacetime is of Petrov type N with respect to the same vector.
Citation: Reviews in Mathematical Physics
PubDate: 20170126T09:11:03Z
DOI: 10.1142/S0129055X17500076
 Authors: Carlo Alberto Mantica, Young Jin Suh
 A cutoff tubular geometry of loop space
 Authors: Partha Mukhopadhyay
Abstract: Reviews in Mathematical Physics, Ahead of Print.
Motivated by the computation of loop space quantum mechanics as indicated in [14], here we seek a better understanding of the tubular geometry of loop space [math] corresponding to a Riemannian manifold [math] around the submanifold of vanishing loops. Our approach is to first compute the tubular metric of [math] around the diagonal submanifold, where [math] is the Cartesian product of [math] copies of [math] with a cyclic ordering. This gives an infinite sequence of tubular metrics such that the one relevant to [math] can be obtained by taking the limit [math]. Such metrics are computed by adopting an indirect method where the general tubular expansion theorem of [21] is crucially used. We discuss how the complete reparametrization isometry of loop space arises in the large[math] limit and verify that the corresponding Killing equation is satisfied to all orders in tubular expansion. These tubular metrics can alternatively be interpreted as some natural Riemannian metrics on certain bundles of tangent spaces of [math] which, for [math], is the tangent bundle [math].
Citation: Reviews in Mathematical Physics
PubDate: 20170117T10:09:27Z
DOI: 10.1142/S0129055X17500064
 Authors: Partha Mukhopadhyay