1,721,069 research outputs found
On generalized Lemaitre–Tolman–Bondi metric: Fractal matter at the end of matter–antimatter recombination
No full textMany recent researches have investigated the deviations from the Friedmannian cosmological model, as well as their consequences on unexplained cosmological phenomena, such as dark matter and the acceleration of the Universe. On one hand, a first-order perturbative study of matter inhomogeneity returned a partial explanation of dark matter and dark energy, as relativistic effects due to the retarded potentials of far objects. On the other hand, the fractal cosmology, now approximated by a Lemaitre–Tolman–Bondi (LTB) metric, results in distortions of the luminosity distances of SNe Ia, explaining the acceleration as apparent. In this work, we extend the LTB metric to ancient times. The origin of the fractal distribution of matter is explained as the matter remnant after the matter–antimatter recombination epoch. We show that the evolution of such a inhomogeneity necessarily requires a dynamical generalization of LTB, and we propose a particular solution
Special Vinberg cones, invariant admissible cubics and special real manifolds
No full textBy Vinberg theory any homogeneous convex cone V may be realised as the cone of positive Hermitian matrices in a T -algebra of generalised
matrices. The level hypersurfaces V_q ⊂ V of homogeneous cubic polynomials
q with positive definite Hessian (symmetric) form g(q) := − Hess(log(q))|_{T V_q}
are the special real manifolds. Such manifolds occur as scalar manifolds of
the vector multiplets in N = 2, D = 5 supergravity and, through the r-map,
correspond to Kaehler scalar manifolds in N = 2 D = 4 supergravity. We offer
a simplified exposition of the Vinberg theory in terms of Nil-algebras (= the
subalgebras of upper triangular matrices in Vinberg T -algebras) and we use it
to describe all rational functions on a special Vinberg cone that are G_0- or G′-
invariant, where G_0 is the unimodular subgroup of the solvable group G acting
simply transitively on the cone, and G′ is the unipotent radical of G_0. The
results are used to determine G_0- and G′-invariant cubic polynomials q that
are admissible (i.e. such that the hypersurface V_q = {q = 1} ∩ V has positive
definite Hessian form g(q)) for rank 2 and rank 3 special Vinberg cones. We
get in this way examples of continuous families of non-homogeneous special
real manifolds of cohomogeneity less than or equal to two
Quantum klein space and superspace
Full text linkWe give an algebraic quantization, in the sense of quantum groups, of the complex Minkowski space, and we examine the real forms corresponding to the signatures (3, 1), (2, 2), (4, 0), constructing the corresponding quantum metrics and providing an explicit presentation of the quantized coordinate algebras. In particular, we focus on the Kleinian signature (2, 2). The quantizations of the complex and real spaces come together with a coaction of the quantizations of the respective symmetry groups. We also extend such quantizations to the N = 1 supersetting
Klein and conformal superspaces, split algebras and spinor orbits
No full text We discuss [Formula: see text] Klein and Klein-conformal superspaces in [Formula: see text] space-time dimensions, realizing them in terms of their functor of points over the split composition algebra [Formula: see text]. 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 [Formula: see text] and [Formula: see text] as [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Within this approach, we also analyze the non-trivial spinor orbit stratification that is relevant in our construction since it affects the Klein-conformal superspace structure. </jats:p
Magic Coset Decompositions
Full text linkBy exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special K\"ahler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal SO(8) covariance. Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed
Classification of four-rebit states
No full textWe classify states of four rebits, that is, we classify the orbits of the group Gˆ(R)=SL(2,R)4 in the space (R2)⊗4. This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the Gˆ(R)-module (R2)⊗4 via a Z/2Z-grading of the simple split real Lie algebra of type D4, the orbits are divided into three groups: semisimple, nilpotent and mixed. The nilpotent orbits have been classified in Dietrich et al. (2017) [26], yielding applications in theoretical physics (extremal black holes in the STU model of N=2,D=4 supergravity, see Ruggeri and Trigiante (2017) [51]). Here we focus on the semisimple and mixed orbits which we classify with recently developed methods based on Galois cohomology, see Borovoi et al. (2021) [8,9]. These orbits are relevant to the classification of non-extremal (or extremal over-rotating) and two-center extremal black hole solutions in the STU model.Fil: Dietrich, Heiko. Monash University; AustraliaFil: de Graaf, Willem A.. Universita degli Studi di Trento; ItaliaFil: Marrani, Alessio. Universidad de Murcia; EspañaFil: Origlia, Marcos Miguel. Monash University; Australia. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin
Classification of four qubit states and their stabilisers under SLOCC operations
Full text linkWe classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)4 on the Hilbert space H4=(C2)⊗4 . We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)4 -orbits on H4 . It follows that an element of (C2)⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)4 . We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4⋉ SL(2,C)4 where Sym4 permutes the four tensor factors of (C2)⊗4 .Fil: Dietrich, Heiko. Monash University; AustraliaFil: De Graaf, Willem A.. Universita degli Studi di Trento; ItaliaFil: Marrani, Alessio. Universidad de Murcia; EspañaFil: Origlia, Marcos Miguel. Monash University; Australia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin
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