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Academic literature on the topic 'Grassmannian Coordinates'

Author: Grafiati
Published: 7 September 2023

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Journal articles on the topic "Grassmannian Coordinates"

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MOHAMMEDI, NOUREDDINE. "FRACTIONAL SUPERSYMMETRY." Modern Physics Letters A 10, no. 18 (June 14, 1995): 1287–91. http://dx.doi.org/10.1142/s021773239500140x.

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A symmetry between bosonic coordinates and some Grassmannian-type coordinates is presented. Commuting two of these Grassmannian-type variables results in an arbitrary phase factor (not just a minus sign). This symmetry is also realized at the level of the field theory.
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Dzhunushaliev, V. "A Geometrical Interpretation of Grassmannian Coordinates." General Relativity and Gravitation 34, no. 8 (August 2002): 1267–75. http://dx.doi.org/10.1023/a:1019782619091.

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Talaska, Kelli. "Combinatorial formulas for -coordinates in a totally nonnegative Grassmannian." Journal of Combinatorial Theory, Series A 118, no. 1 (January 2011): 58–66. http://dx.doi.org/10.1016/j.jcta.2009.10.006.

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DELBOURGO, R., S. TWISK, and R. B. ZHANG. "GRAND UNIFICATION AND GRASSMANNIAN KALUZA-KLEIN THEORY." Modern Physics Letters A 03, no. 11 (September 1988): 1073–78. http://dx.doi.org/10.1142/s0217732388001264.

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It is possible to construct a grand unified model, including gravity, by adjoining further anticommuting coordinates to space-time. We carry out this program for SU(5) and SO(10) unified models; curiously, the former is much more economical than the latter and simply requires five complex Grassmann variables ξm in addition to the four xμ.
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Purbhoo, Kevin. "Total Nonnegativity and Stable Polynomials." Canadian Mathematical Bulletin 61, no. 4 (November 20, 2018): 836–47. http://dx.doi.org/10.4153/cmb-2018-006-7.

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AbstractWe consider homogeneous multiaffine polynomials whose coefficients are the Plücker coordinates of a point V of the Grassmannian. We show that such a polynomial is stable (with respect to the upper half plane) if and only if V is in the totally nonnegative part of the Grassmannian. To prove this, we consider an action of matrices on multiaffine polynomials. We show that a matrix A preserves stability of polynomials if and only if A is totally nonnegative. The proofs are applications of classical theory of totally nonnegative matrices, and the generalized Pólya–Schur theory of Borcea and Brändén.
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Delbourgo, Robert. "Grassmannian duality and the particle spectrum." International Journal of Modern Physics A 31, no. 26 (September 20, 2016): 1650153. http://dx.doi.org/10.1142/s0217751x16501530.

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Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the classification group [Formula: see text], which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge [Formula: see text] and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain [Formula: see text] which is not far from the experimental value around the [Formula: see text] mass.
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VISWANATHAN, K. S., and R. PARTHASARATHY. "EXTRINSIC GEOMETRY OF WORLD-SHEET SUPERSYMMETRY THROUGH GENERALIZED SUPER-GAUSS MAPS." International Journal of Modern Physics A 07, no. 24 (September 30, 1992): 5995–6011. http://dx.doi.org/10.1142/s0217751x92002714.

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The extrinsic geometry of N=1 world-sheet supersymmetry is studied through generalized super-Gauss map. The world sheet, realized as a conformally immersed super-Riemann surface S in Rn (n=3 is studied for simplicity) is mapped into the supersymmetric Grassmannian G2,3. In order for the Grassmannian fields to form (super) tangent planes to S, certain integrability conditions are satisfied by G2,n fields. These conditions are explicitly derived. The supersymmetric invariant action for the Kähler σ-model G2,3 is reexpressed in terms of the world-sheet coordinates, thereby an off-shell supersymmetric generalization of the action proportional to the extrinsic curvature of the immersed surface is obtained.
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LOSEV, A., and A. TURBINER. "MULTIDIMENSIONAL EXACTLY SOLVABLE PROBLEMS IN QUANTUM MECHANICS AND PULLBACKS OF AFFINE COORDINATES ON THE GRASSMANNIAN." International Journal of Modern Physics A 07, no. 07 (March 20, 1992): 1449–65. http://dx.doi.org/10.1142/s0217751x92000636.

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Multidimensional exactly solvable problems related to compact hidden-symmetry groups are discussed. Natural coordinates on homogeneous space are introduced. It is shown that a potential and scalar curvature of the problem considered have quite a simple form of quadratic polynomials in these coordinates. A mysterious relation between the potential and the curvature observed for SU(2) in Refs. 2 and 3 is obtained in a simple way.
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BENZAIR, H., M. MERAD, and T. BOUDJEDAA. "NONCOMMUTATIVE PATH INTEGRAL FOR SPINLESS RELATIVISTIC EQUATION IN THE TWO-COMPONENT THEORY." Modern Physics Letters A 28, no. 32 (October 6, 2013): 1350144. http://dx.doi.org/10.1142/s0217732313501447.

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In this paper, we have constructed the Green function of the Feshbach–Villars (FV) spinless particle in a noncommutative (NC) phase-space coordinates, where the Pauli matrices describing the charge symmetry are replaced by the Grassmannian odd variables. Subsequently, for the perform calculations, we diagonalize the Hamiltonian governing the dynamics of the system via the Foldy–Wouthuysen (FW) canonical transformation. The exact calculations have been done in the cases of free particle and magnetic field interaction. In both cases, the energy eigenvalues and their corresponding eigenfunctions are deduced.
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Fioresi, Rita, María A. Lledó, and Junaid Razzaq. "Quantum Chiral Superfields." Journal of Physics: Conference Series 2531, no. 1 (June 1, 2023): 012015. http://dx.doi.org/10.1088/1742-6596/2531/1/012015.

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Abstract We define the ordinary Minkowski space inside the conformal space according to Penrose and Manin as homogeneous spaces for the Poincaré and conformal group respectively. We realize the supersymmetric (SUSY) generalizations of such homogeneous spaces over the complex and the real fields. We finally investigate chiral (antichiral) superfields, which are superfields on the super Grassmannian, Gr(2|1, 4|1), respectively on Gr(2|0, 4|1). They ultimately give the twistor coordinates necessary to describe the conformal superspace as the flag Fl(2|0, 2|1; 4|1) and the Minkowski superspace as its big cell.
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Dissertations / Theses on the topic "Grassmannian Coordinates"

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Maltoni, Elena. "Varietà di Grassmann." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20634/.

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Questa tesi è dedicata allo studio delle varietà di Grassmann, ossia varietà proiettive che parametrizzano i sottospazi proiettivi di uno spazio proiettivo dato. Si affronta l'argomento partendo dalla grassmanniana G(1,3) delle rette di P^3 che attraverso le coordinate pluckeriane di una retta di P^3 può essere identificata con una ipersuperficie di P^5 chiamata quadrica di Klein. Studiando tale quadrica è possibile ottenere molte informazioni riguardo famiglie di rette e piani di P^3. Successivamente si introducono le coordinate di Grassmann e si studia la grassmanniana G(h,n), osservando in particolare che essa può essere vista come una sottovarietà proiettiva di un certo spazio proiettivo P^N, definita da polinomi omogenei di grado 2. La trattazione si conclude soffermandosi in particolare sulla varietà G(1,n).
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Book chapters on the topic "Grassmannian Coordinates"

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Scholze, Peter, and Jared Weinstein. "Families of affine Grassmannians." In Berkeley Lectures on p-adic Geometry, 182–90. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202082.003.0020.

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This chapter studies families of affine Grassmannians. In the geometric case, if X is a smooth curve over a field k, Beilinson-Drinfeld defined a family of affine Grassmannians whose fiber parametrizes G-torsors on X. If one fixes a coordinate at x, this gets identified with the affine Grassmannian considered previously. Over fibers with distinct points xi, one gets a product of n copies of the affine Grassmannian, while over fibers with all points xi = x equal, one gets just one copy of the affine Grassmannian: This is possible as the affine Grassmannian is infinite-dimensional. However, sometimes it is useful to remember more information when the points collide. The chapter then discusses the convolution affine Grassmannian in the setting of the previous lecture.
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Conference papers on the topic "Grassmannian Coordinates"

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Zorba, Nizar, and Hossam S. Hassanein. "Grassmannian beamforming for Coordinated Multipoint transmission in multicell systems." In 2013 IEEE 38th Conference on Local Computer Networks Workshops (LCN Workshops). IEEE, 2013. http://dx.doi.org/10.1109/lcnw.2013.6758499.

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