Castro Perelman, Carlos On Clifford multivector-valued actions, generalized Dirac equation and quantization of branes. (English) Zbl 07962390 Complex Var. Elliptic Equ. 70, No. 1, 93-103 (2025). MSC: 81Q05 15A66 53D42 70S05 83C05 × Cite Format Result Cite Review PDF Full Text: DOI
Eelbode, David; Muarem, Guner Branching symplectic monogenics using a Mickelsson-Zhelobenko algebra. (English) Zbl 07928307 Ptak, Marek (ed.) et al., Operator and matrix theory, function spaces, and applications. Proceedings of the 33rd international workshop on operator theory and its applications, IWOTA 2022, Kraków, Poland, September 6–10, 2022. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 295, 175-187 (2024). MSC: 17B10 15A66 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Eelbode, David; Muarem, Guner A Hermitian refinement of symplectic Clifford analysis. (English) Zbl 07926838 Math. Methods Appl. Sci. 47, No. 14, 11473-11489 (2024). MSC: 15A66 42B37 32A50 17B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shirokov, Dmitry On SVD and polar decomposition in real and complexified Clifford algebras. (English) Zbl 1543.15015 Adv. Appl. Clifford Algebr. 34, No. 3, Paper No. 23, 20 p. (2024). MSC: 15A66 15A18 15A67 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pavšič, Matej A new perspective on quantum field theory revealing possible existence of another kind of fermions forming dark matter. (English) Zbl 1540.81088 Int. J. Geom. Methods Mod. Phys. 19, No. 12, Article ID 2250184, 50 p. (2022). MSC: 81T10 81T08 81S08 81S10 78A20 81V74 83C56 15A66 26B40 81Q12 15B33 51F25 81V15 81V05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anglès, Pierre Siegel-Satake cross and associated Clifford algebras. (English) Zbl 1506.11059 Adv. Appl. Clifford Algebr. 32, No. 5, Paper No. 53, 28 p. (2022). Reviewer: Meinhard Peters (Münster) MSC: 11E88 15A63 15A66 53D05 11F46 × Cite Format Result Cite Review PDF Full Text: DOI
Tan, Xinyu; Rengaswamy, Narayanan; Calderbank, Robert Approximate unitary 3-designs from transvection Markov chains. (English) Zbl 1504.81064 Des. Codes Cryptography 90, No. 9, 2181-2204 (2022). MSC: 81P68 68P30 05C25 28C10 60J22 15A66 05C90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Burchell, Timothy J.; Bridges, Thomas J. Symplectic transversality and the Pego-Weinstein theory. (English) Zbl 1504.35422 Adv. Math. 406, Article ID 108524, 58 p. (2022). MSC: 35Q41 35Q51 35C08 37C29 15A66 35B40 53D05 76B25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Eelbode, David; Muarem, Guner The orthogonal branching problem for symplectic monogenics. (English) Zbl 1495.17008 Adv. Appl. Clifford Algebr. 32, No. 3, Paper No. 32, 26 p. (2022). Reviewer: Adam Chapman (Tel Hai) MSC: 17B10 15A66 15A67 53D05 22E47 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Fabbri, Luca; Rogerio, Rodolfo José Bueno Most general propagator in quantum field theory. (English) Zbl 1487.81126 Mod. Phys. Lett. A 36, No. 19, Article ID 2150124, 19 p. (2021). MSC: 81T10 81Q05 81R25 15A66 51A50 47A10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grützmann, Melchior; Michel, Jean-Philippe; Xu, Ping Weyl quantization of degree 2 symplectic graded manifolds. (English. French summary) Zbl 1481.53105 J. Math. Pures Appl. (9) 154, 67-107 (2021). Reviewer: Andrea Galasso (Taipei) MSC: 53D17 53D18 53D55 81S10 16W70 15A66 17B63 53B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Karakhanyan, D.; Kirschner, R. Spinorial \(R\) operator and algebraic Bethe ansatz. (English) Zbl 1472.81120 Nucl. Phys., B 951, Article ID 114905, 24 p. (2020). MSC: 81R25 15A66 16T25 51A50 14D05 82B20 81Q40 82B23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bhunia, Sushil; Mahalanobis, Ayan; Shinde, Pralhad; Singh, Anupam Algorithms in linear algebraic groups. (English) Zbl 1458.20038 Adv. Appl. Clifford Algebr. 30, No. 3, Paper No. 31, 23 p. (2020). Reviewer: Erich W. Ellers (Toronto) MSC: 20G05 11E57 15A21 15A66 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Yicao Toric generalized Kähler structures. III. (English) Zbl 1437.53063 J. Geom. Phys. 151, Article ID 103634, 15 p. (2020). Reviewer: Nicolai K. Smolentsev (Kemerovo) MSC: 53D18 15A66 53C55 32Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Calixto, Manuel Massive conformal particles with non-abelian charges from free \(\text{U}(2N, 2N)\)-twistor dynamics: quantization and coherent states. (English) Zbl 1423.81102 J. Geom. Phys. 146, Article ID 103505, 14 p. (2019). MSC: 81R30 81R05 81R25 81S10 32Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
De Bie, Hendrik; Holíková, Marie; Somberg, Petr Basic aspects of symplectic Clifford analysis for the symplectic Dirac operator. (English) Zbl 1367.53042 Adv. Appl. Clifford Algebr. 27, No. 2, 1103-1132 (2017). MSC: 53C27 53D05 81R25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dargys, A.; Acus, A. Calculation of quantum eigens with geometrical algebra rotors. (English) Zbl 1367.15011 Adv. Appl. Clifford Algebr. 27, No. 1, 241-253 (2017). MSC: 15A18 15A66 65F15 65P10 81P68 81R25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sam, Steven V.; Snowden, Andrew Infinite rank spinor and oscillator representations. (English) Zbl 1370.15024 J. Comb. Algebra 1, No. 2, 145-183 (2017). Reviewer: Rabe von Randow (Bonn) MSC: 15A66 05E05 15A69 20G05 15A72 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krýsl, Svatopluk Symplectic spinors and Hodge theory. arXiv:1708.02026 Preprint, arXiv:1708.02026 [math.DG] (2017). MSC: 15A66 53C07 53C10 53D05 53D35 58A14 81S10 11F27 × Cite Format Result Cite Full Text: arXiv OA License
Johnson-Freyd, Theo The quaternions and Bott periodicity are quantum Hamiltonian reductions. (English) Zbl 1354.15016 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 116, 6 p. (2016). MSC: 15A66 53D20 16D90 81Q60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gorodentsev, Alexey L. Algebra I. Textbook for students of mathematics. Translated from the Russian. Originally published by MCCME, Moscow, 2013. (English) Zbl 1359.15001 Cham: Springer (ISBN 978-3-319-45284-5/hbk; 978-3-319-45285-2/ebook). xx, 564 p. (2016). Reviewer: John D. Dixon (Ottawa) MSC: 15-01 13-01 14-01 20-01 × Cite Format Result Cite Review PDF Full Text: DOI
Castro, Carlos A unified description of particles, strings and branes in Clifford spaces and \(p\)-brane/polyparticle duality. (English) Zbl 1334.83063 Int. J. Geom. Methods Mod. Phys. 13, No. 1, Article ID 1550133, 13 p. (2016). MSC: 83E30 81T30 81S10 15A66 81T40 35L05 83C45 × Cite Format Result Cite Review PDF Full Text: DOI
Xambó-Descamps, Sebastià Book review of: D. Hestenes, Space-time algebra. Foreword by Anthony Lasenby. 2nd ed. (English) Zbl 1334.00076 Eur. Math. Soc. Newsl. 98, 63-66 (2015). MSC: 00A17 83-02 83C05 53-02 53C27 81R25 53B30 83C60 53Z05 01A75 15A66 11R52 83A05 81S10 × Cite Format Result Cite Review PDF
Shirokov, D. S. Symplectic, orthogonal and linear Lie groups in Clifford algebra. (English) Zbl 1323.15015 Adv. Appl. Clifford Algebr. 25, No. 3, 707-718 (2015). MSC: 15A66 11E88 22E99 17B99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kanatchikov, Igor V. Ehrenfest theorem in precanonical quantization. (English) Zbl 1316.81085 J. Geom. Symmetry Phys. 37, 43-66 (2015). MSC: 81T70 81T20 70S05 15A66 81T13 81S10 53D42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hestenes, David [Lasenby, Anthony] Space-time algebra. With a foreword by Anthony Lasenby. 2nd ed. (English) Zbl 1316.83005 Cham: Birkhäuser/Springer (ISBN 978-3-319-18412-8/hbk; 978-3-319-38688-1/pbk; 978-3-319-18413-5/ebook). xxiv, 102 p. (2015). Reviewer: Hans-Jürgen Schmidt (Potsdam) MSC: 83-02 83C05 53-02 53C27 81R25 53B30 83C60 53Z05 01A75 15A66 11R52 83A05 81S10 × Cite Format Result Cite Review PDF Full Text: DOI
Cooperstein, Bruce N. Advanced linear algebra. 2nd edition. (English) Zbl 1319.15001 Textbooks in Mathematics. Boca Raton, FL: CRC Press (ISBN 978-1-4822-4884-5/hbk). xxvii, 594 p. (2015). Reviewer: Rabe von Randow (Bonn) MSC: 15-01 15A03 15A04 15A06 15A21 15A69 15A63 15A15 65F20 15A66 20Gxx 15A09 15A42 68P10 15A60 94B05 15B48 × Cite Format Result Cite Review PDF
Brackx, F.; De Schepper, H.; Eelbode, D.; Lávička, R.; Souček, V. Fundaments of quaternionic Clifford analysis. I: Quaternionic structure. (English) Zbl 1364.15016 Adv. Appl. Clifford Algebr. 24, No. 4, 955-980 (2014). Reviewer: Eckhard Hitzer (Tokyo) MSC: 15A66 30A05 20G20 32A10 15B57 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Koenig, Robert; Smolin, John A. How to efficiently select an arbitrary Clifford group element. (English) Zbl 1308.81060 J. Math. Phys. 55, No. 12, 122202, 12 p. (2014). Reviewer: Carlos F. Lardizabal (Porto Alegre) MSC: 81P68 15A66 22E70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cahen, Michel; Gutt, Simone; La Fuente Gravy, Laurent; Rawnsley, John On \(Mp^{\operatorname{c}}\)-structures and symplectic Dirac operators. (English) Zbl 1325.53066 J. Geom. Phys. 86, 434-466 (2014). MSC: 53C27 53D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brackx, F.; De Schepper, H.; Eelbode, D.; Lávička, R.; Souček, V. Fischer decomposition in symplectic harmonic analysis. (English) Zbl 1337.15021 Ann. Global Anal. Geom. 46, No. 4, 409-430 (2014). Reviewer: Wolfgang Sprößig (Freiberg) MSC: 15A66 30G35 43A50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Moroianu, Andrei; Semmelmann, Uwe Generalized Killing spinors and Lagrangian graphs. (English) Zbl 1309.53041 Differ. Geom. Appl. 37, 141-151 (2014). MSC: 53C27 53C42 53C25 53D12 53D25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
González-Jiménez, L.; Carbajal-Espinosa, O.; Loukianov, A.; Bayro-Corrochano, E. Robust pose control of robot manipulators using conformal geometric algebra. (English) Zbl 1297.93119 Adv. Appl. Clifford Algebr. 24, No. 2, 533-552 (2014). MSC: 93C85 70E60 15A66 53A30 70G45 93B12 × Cite Format Result Cite Review PDF Full Text: DOI
Castro, Carlos Super-Clifford gravity, higher spins, generalized supergeometry and much more. (English) Zbl 1298.83105 Adv. Appl. Clifford Algebr. 24, No. 1, 55-69 (2014). MSC: 83D05 83E50 15A66 81V22 17B45 × Cite Format Result Cite Review PDF Full Text: DOI
Cahen, Michel; Gutt, Simone \(\mathrm{Spin}^c\), \(\mathrm{Mp}^c\) and symplectic Dirac operators. (English) Zbl 1403.53064 Kielanowski, Piotr (ed.) et al., Geometric methods in physics. XXXI workshop, Białowieża, Poland, June 24–30, 2012. Selected papers based on the presentations at the workshop. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0644-2/hbk; 978-3-0348-0645-9/ebook). Trends in Mathematics, 13-28 (2013). MSC: 53D05 58J60 81S10 × Cite Format Result Cite Review PDF Full Text: DOI
Klein, Andreas Symplectic spinors, holonomy and Maslov index. (English) Zbl 1275.53073 Rend. Circ. Mat. Palermo (2) 62, No. 2, 285-300 (2013). MSC: 53D12 53D05 53C29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yefremov, Alexander P. Pre-geometric structure of quantum and classical particles in terms of quaternion spinors. (English) Zbl 1272.83020 Gravit. Cosmol. 19, No. 2, 71-78 (2013). MSC: 83C10 83E05 83C60 81S10 11R52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Binz, Ernst; de Gosson, Maurice A.; Hiley, Basil J. Clifford algebras in symplectic geometry and quantum mechanics. (English) Zbl 1276.81065 Found. Phys. 43, No. 4, 424-439 (2013). Reviewer: Benjamin Cahen (Metz) MSC: 81Q70 15A66 35R03 53D05 17B63 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Miyaoka, Reiko Moment maps of the spin action and the Cartan-Münzner polynomials of degree four. (English) Zbl 1267.53057 Math. Ann. 355, No. 3, 1067-1084 (2013). Reviewer: Simona Costache (Bucuresti) MSC: 53C40 53D20 15A66 × Cite Format Result Cite Review PDF Full Text: DOI
Abou El Dahab, E. T. Application of geometric algebra to generalized Hamiltonian (Birkhoffian) mechanics. (English) Zbl 1339.70031 Clifford Anal. Clifford Algebr. Appl. 1, No. 1, 41-48 (2012). MSC: 70H05 15A66 37J05 81S05 × Cite Format Result Cite Review PDF
Miyaoka, Reiko Isoparametric hypersurfaces and moment map. (English) Zbl 1260.53103 Suh, Young Jin (ed.) et al., Proceedings of the 16th international workshop on differential geometry and the 5th KNUGRG-OCAMI differential geometry workshop, Taegu, Korea, October 31–November 3, 2012. Taegu: National Institute for Mathematical Sciences and Grassmann Research Group. 11-23 (2012). MSC: 53C40 53C24 53D20 15A66 × Cite Format Result Cite Review PDF
Pavšič, Matej A theory of quantized fields based on orthogonal and symplectic Clifford algebras. (English) Zbl 1259.83011 Adv. Appl. Clifford Algebr. 22, No. 2, 449-481 (2012). MSC: 83C45 83E30 83E15 15A66 81V22 81T20 81S10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yefremov, A. P. Fundamental properties of quaternion spinors. (English) Zbl 1258.83040 Gravit. Cosmol. 18, No. 3, 188-195 (2012). MSC: 83C60 11R52 81S10 83A05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krýsl, Svatopluk Howe duality for the metaplectic group acting on symplectic spinor valued forms. (English) Zbl 1275.17015 J. Lie Theory 22, No. 4, 1049-1063 (2012). MSC: 17B10 22E46 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Cahen, Michel; Gutt, Simone; Rawnsley, John Symplectic Dirac operators and \({Mp^{\text c}}\)-structures. (English) Zbl 1270.81117 Gen. Relativ. Gravitation 43, No. 12, 3593-3617 (2011). MSC: 81S10 83C47 81Q05 81R25 53C15 53D05 81Q35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krýsl, Svatopluk Complex of twistor operators in symplectic spin geometry. (English) Zbl 1203.53024 Monatsh. Math. 161, No. 4, 381-398 (2010). Reviewer: Radu Miron (Iaşi) MSC: 53C07 53D05 58J10 53C28 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Goto, Ryushi Deformations of generalized complex generalized Kähler structures. (English) Zbl 1201.53085 J. Differ. Geom. 84, No. 3, 525-560 (2010). Reviewer: Valentino Tosatti (New York) MSC: 53D18 32Q15 53D05 53C56 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Krýsl, Svatopluk Structure of the curvature tensor on symplectic spinors. (English) Zbl 1406.53025 J. Geom. Phys. 60, No. 9, 1251-1261 (2010). MSC: 53C07 53D05 58J10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Agricola, Ilka; Friedrich, Thomas 3-Sasakian manifolds in dimension seven, their spinors and G\(_2\)-structures. (English) Zbl 1188.53041 J. Geom. Phys. 60, No. 2, 326-332 (2010). Reviewer: Zbigniew Olszak (Wrocław) MSC: 53C25 53D15 81T30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alekseev, A.; Bursztyn, H.; Meinrenken, E. Pure spinors on Lie groups. (English) Zbl 1251.53052 Dai, Xianzhe (ed.) et al., From probability to geometry I. Volume in honor of the 60th birthday of Jean-Michel Bismut. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-288-4/pbk). Astérisque 327, 131-199 (2009). Reviewer: Akira Yoshioka (Tokyo) MSC: 53D17 53D20 15A66 53C30 53C27 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Krýsl, Svatopluk Symplectic Dirac operator and its generalization. (English) Zbl 1181.81079 Adv. Appl. Clifford Algebr. 18, No. 3-4, 853-863 (2008). MSC: 81S10 17B10 17B20 53D10 81R25 22E70 81R20 × Cite Format Result Cite Review PDF Full Text: DOI
Khrennikov, Andrei Hyperbolic quantization. (English) Zbl 1181.81078 Adv. Appl. Clifford Algebr. 18, No. 3-4, 843-852 (2008). MSC: 81S10 15A66 46N50 32W25 53D55 × Cite Format Result Cite Review PDF Full Text: DOI
Conradt, Oliver Mathematical physics in space and counterspace. 2nd ed. (English) Zbl 1176.51007 Arbeitshefte der Mathematisch-Astronomischen Sektion am Goetheanum. Kleine Reihe 4. Dornach: Verlag am Goetheanum; Basel: Univ. Basel (Diss. 2000) (ISBN 978-3-7235-1333-0/pbk). xii, 200 p. (2008). MSC: 51P05 83A05 51-02 15A66 70G55 70H15 × Cite Format Result Cite Review PDF
Krýsl, Svatopluk Symplectic Dirac operator and its higher spin analogues. (English) Zbl 1166.58305 Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2008, Psalidi, Kos, Greece, 16–20 September 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0576-9/hbk). AIP Conference Proceedings 1048, 674-677 (2008). MSC: 58J05 58J50 35N10 53D05 × Cite Format Result Cite Review PDF
Krýsl, Svatopluk Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds. (English) Zbl 1199.58011 Arch. Math., Brno 43, No. 5, 467-484 (2007). MSC: 58J05 58J50 35N10 53D05 × Cite Format Result Cite Review PDF Full Text: EuDML EMIS
Krýsl, Svatopluk Decomposition of a tensor product of a higher symplectic spinor module and the defining representation of \(\mathrm{sp}(2n,\mathbb C)\). (English) Zbl 1120.17006 J. Lie Theory 17, No. 1, 63-72 (2007). Reviewer: Joseph D. Zund (Las Cruces) MSC: 17B10 17B81 22E47 × Cite Format Result Cite Review PDF Full Text: Link
Clerc, Jean-Louis; Koufany, Khalid A primitive of the generalized Maslov cocycle. (Primitive du cocycle de Maslov généralisé.) (French) Zbl 1110.32009 Math. Ann. 337, No. 1, 91-138 (2007). Reviewer: Gabriela P. Ovando (Santa Fé) MSC: 32M15 53D12 15A66 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krýsl, Svatopluk Symplectic spinor valued forms and invariant operators acting between them. (English) Zbl 1164.58320 Arch. Math., Brno 42, No. 5, 279-290 (2006). MSC: 58J60 53C27 53D05 × Cite Format Result Cite Review PDF Full Text: arXiv EuDML EMIS
Krýsl, Svatopluk On a distinguished class of infinite dimensional representations of \(\mathfrak{sp}(2n,\mathbb C)\). (English) Zbl 1100.15014 Slovák, Jan (ed.) et al., The proceedings of the 24th winter school “Geometry and physics”, Srní, Czech Republic, January 17–24, 2004. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 75, 269-277 (2005). MSC: 15A66 17B10 15A69 53C27 × Cite Format Result Cite Review PDF
Kisil, Vladimir V. \(p\)-mechanics and field theory. (English) Zbl 1088.81067 Rep. Math. Phys. 56, No. 2, 161-174 (2005). Reviewer: Benjamin Cahen (Metz) MSC: 81S10 81R05 81R15 53D17 53D55 43A65 15A66 81T70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mostafazadeh, Ali Classical and quantum fermions linked by an algebraic deformation. (English) Zbl 1082.81078 Int. J. Geom. Methods Mod. Phys. 2, No. 5, 777-782 (2005). MSC: 81T70 81S10 53D55 15A66 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Henselder, Peter; Hirshfeld, Allen C.; Spernat, Thomas Star products and geometric algebra. (English) Zbl 1084.81045 Ann. Phys. 317, No. 1, 107-129 (2005). Reviewer: Benjamin Cahen (Metz) MSC: 81S10 53D55 15A66 81S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hirshfeld, Allen C.; Henselder, Peter; Spernat, Thomas Cliffordization, spin, and fermionic star products. (English) Zbl 1074.81037 Ann. Phys. 314, No. 1, 75-98 (2004). MSC: 81S10 53D55 15A66 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bartsch, T. The Kustaanheimo-Stiefel transformation in geometric algebra. (English) Zbl 1167.70312 J. Phys. A, Math. Gen. 36, No. 25, 6963-6978 (2003). MSC: 70F05 15A66 70F15 70H15 78A30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Colin de Verdière, Yves The level crossing problem in semi-classical analysis. I: The symmetric class. (English) Zbl 1113.35151 Ann. Inst. Fourier 53, No. 4, 1023-1054 (2003). MSC: 35S30 35C20 35Q40 47G30 81Q20 81R30 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Friedrich, Thomas; Ivanov, Stefan Almost contact manifolds, connections with torsion, and parallel spinors. (English) Zbl 1035.53058 J. Reine Angew. Math. 559, 217-236 (2003). Reviewer: J. D. Zund (Las Cruces) MSC: 53C25 53C27 81T30 53D15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sommen, Frank Analysis using abstract vector variables. (English) Zbl 1028.15029 Dorst, Leo (ed.) et al., Applications of geometric algebra in computer science and engineering. Papers from the conference, AGACSE 2001, Cambridge, UK, July 9-13, 2001. Boston, MA: Birkhäuser. 119-128 (2002). MSC: 15A66 × Cite Format Result Cite Review PDF
Meinrenken, E. Clifford algebras and the Duflo isomorphism. (English) Zbl 1020.17007 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press. 637-642 (2002). MSC: 17B35 53D20 17B80 15A66 55N91 × Cite Format Result Cite Review PDF Full Text: arXiv
Baker, Andrew Matrix groups. An introduction to Lie group theory. (English) Zbl 1009.22001 Springer Undergraduate Mathematics Series. London: Springer. xi, 330 p. (2002). Reviewer: A.Akutowicz (Berlin) MSC: 22-01 57-01 22E46 17-01 15A66 × Cite Format Result Cite Review PDF
López Almorox, Antonio; Tejero Prieto, Carlos Symplectic reduction on the hyperbolic Kustaanheimo-Stiefel fibration. (English) Zbl 1031.53116 del Olmo Martínez, Mariano A. (ed.) et al., Proceedings of the 8th fall workshop on geometry and physics, Medina del Campo, Spain, September 23-25, 1999. Madrid: Real Sociedad Matemática Española. Publ. R. Soc. Mat. Esp. 2, 153-168 (2001). Reviewer: Andrew Bucki (Oklahoma City) MSC: 53D20 70H33 70G45 15A66 × Cite Format Result Cite Review PDF
Tyutin, I. V. General form of the \(*\)-product on the Grassmann algebra. (English. Russian original) Zbl 1027.81018 Theor. Math. Phys. 127, No. 2, 619-631 (2001); translation from Teor. Mat. Fiz. 127, No. 2, 253-267 (2001). MSC: 81S10 53D55 15A75 15A66 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Seeger, Lutz Metrics with harmonic spinors on even dimensional spheres. (Metriken mit harmonischen Spinoren auf geradedimensionalen Sphären.) (German) Zbl 0986.53018 Berichte aus der Mathematik. Aachen: Shaker Verlag. Hamburg: Univ. Hamburg, Fachbereich Mathematik (Diss.), 86 S. (2001). Reviewer: Christian Bär (Hamburg) MSC: 53C27 × Cite Format Result Cite Review PDF
Vargas, José Gabriel; Torr, Douglas Graham Marriage of Clifford algebra and Finsler geometry: A lineage for unification? (English) Zbl 0979.53084 Int. J. Theor. Phys. 40, No. 1, 275-298 (2001). MSC: 53C80 83E15 81S10 53D50 53C60 15A66 53B15 53C05 × Cite Format Result Cite Review PDF Full Text: DOI
Bajguz, W. On \(Z_n\) quantum mechanics. (English) Zbl 0982.15036 Czech. J. Phys. 50, No. 1, 11-15 (2000). MSC: 15A66 15A90 81S10 × Cite Format Result Cite Review PDF Full Text: DOI
Yamaleev, Robert M. From generalized Clifford algebras to Nambu’s formulation of dynamics. (English) Zbl 0973.15023 Adv. Appl. Clifford Algebr. 10, No. 1, 15-38 (2000). Reviewer: Jürgen Tolksdorf (Mannheim) MSC: 15A66 37J05 70H05 × Cite Format Result Cite Review PDF Full Text: DOI
Hannabuss, K. C. Highest weights, projective geometry, and the classical limit. I: Geometrical aspects and the classical limit. (English) Zbl 0948.22015 J. Geom. Phys. 34, No. 1, 1-28 (2000). Reviewer: R.Bödi (Tübingen) MSC: 22E46 51A50 81S10 15A66 81R50 × Cite Format Result Cite Review PDF Full Text: DOI
Habermann, Katharina Symplectic Dirac operators of Kähler manifolds. (English) Zbl 0965.58025 Math. Nachr. 211, 37-62 (2000). Reviewer: Sebastian Goette (Tübingen) MSC: 58J50 53C55 35P15 35K05 58J35 58J05 53D50 53C35 × Cite Format Result Cite Review PDF Full Text: DOI
Kwaśniewski, A. K. On generalized Clifford algebra \(C_4^{(n)}\) and \(GL_q (2; \mathbb{C})\) quantum group. (English) Zbl 0958.15024 Adv. Appl. Clifford Algebr. 9, No. 2, 249-260 (1999). Reviewer: Wolfgang Sproessig (Freiberg) MSC: 15A66 81R50 81S10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shuster, Eugene Killing spinors and supersymmetry on AdS. (English) Zbl 0951.83025 Nucl. Phys., B 554, No. 1-2, 198-214 (1999). MSC: 83C60 83E50 81T60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grosse, H.; Strohmaier, Alexander Noncommutative geometry and the regularization problem of 4D quantum field theory. (English) Zbl 0957.81090 Lett. Math. Phys. 48, No. 2, 163-179 (1999). MSC: 81T75 81T10 81S10 46L87 58B34 17B81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Graham, William; Vogan, David A. jun. Geometric quantization for nilpotent coadjoint orbits. (English) Zbl 0886.22008 Tirao, Juan (ed.) et al., Geometry and representation theory of real and \(p\)-adic groups. Papers from the 5th workshop on representation theory of Lie groups and its applications, Córdoba, Argentina, August 1995. Boston, MA: Birkhäuser. Prog. Math. 158, 69-137 (1998). Reviewer: C.Udrişte (Bucureşti) MSC: 22E46 81S10 37J99 × Cite Format Result Cite Review PDF
Habermann, K. Harmonic symplectic spinors on Riemann surfaces. (English) Zbl 0892.53016 Manuscr. Math. 94, No. 4, 465-484 (1997). Reviewer: J.D.Zund (Las Cruces) MSC: 53C15 53D05 58J60 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Nicolaescu, Liviu I. Generalized symplectic geometries and the index of families of elliptic problems. (English) Zbl 0903.35015 Mem. Am. Math. Soc. 609, 80 p. (1997). Reviewer: Z.G.Sheftel’ (Clausthal-Zellerfeld) MSC: 35J15 47A53 58-02 58J20 58J05 15A66 55N15 × Cite Format Result Cite Review PDF Full Text: DOI
Baylis, William E. Eigenspinors in curved spacetime. (English) Zbl 0861.15037 Baylis, William E. (ed.), Clifford (geometric) algebras with applications to physics, mathematics, and engineering. Proceedings of the 1995 summer school on theoretical physics, held in Banff, Canada, July 30–August 12, 1995. Boston, MA: Birkhäuser. 285-296 (1996). MSC: 15A66 15A90 83C60 × Cite Format Result Cite Review PDF
Adem, José; Ławrynowicz, Julian; Rembieliński, Jakub Generalized Hurwitz maps of the type \(S\times V\to W\). (English) Zbl 0885.15019 Rep. Math. Phys. 37, No. 1-3, 325-336 (1996). Reviewer: E.Ellers (Toronto) MSC: 15A63 15A66 × Cite Format Result Cite Review PDF Full Text: DOI
Habermann, Katharina The Dirac operator on symplectic spinors. (English) Zbl 0842.58042 Ann. Global Anal. Geom. 13, No. 2, 155-168 (1995). Reviewer: H.Baum (Berlin) MSC: 53D50 81S10 53D05 × Cite Format Result Cite Review PDF Full Text: DOI
Kammerer, Jean-Bertrand; Valton, Michel Representation of a quantum particle with \(\text{spin}1/2\) by means of the Moyal product and a flat symplectic supermanifold. (Représentation d’une particule quantique de \(\text{spin}1/2\) par le produit de Moyal et une super-variété symplectique plate.) (French) Zbl 0796.58019 J. Geom. Phys. 13, No. 4, 393-414 (1994). MSC: 37J99 81V25 58A50 17B65 15A66 15A75 × Cite Format Result Cite Review PDF Full Text: DOI
Burlakov, M. P.; Evtushik, L. E. Clifford’s structure and Clifford’s differentiation on Riemannian spaces. (English. Russian original) Zbl 0904.53017 Mosc. Univ. Math. Bull. 49, No. 2, 61-66 (1994); translation from Vestn. Mosk. Univ., Ser. I 1994, No. 2, 67-74 (1994). Reviewer: Z.Jankovsky (Praha) MSC: 53B20 70G45 53B30 15A66 × Cite Format Result Cite Review PDF
Pappas, Richard C. A formulation of Hamiltonian mechanics using geometric calculus. (English) Zbl 0833.70013 Brackx, F. (ed.) et al., Clifford algebras and their applications in mathematical physics. Proceedings of the third conference held at Deinze, Belgium, 1993. Dordrecht: Kluwer Academic Publishers. Fundam. Theor. Phys. 55, 251-258 (1993). MSC: 70H05 70G45 15A66 × Cite Format Result Cite Review PDF
Hu, Yaozhong Fermionic hypercontractivity, after Carlen-Lieb. (Hypercontractivité pour les fermions, d’après Carlen-Lieb.) (French) Zbl 0810.46072 Azéma, J. (ed.) et al., Séminaire de probabilités XXVII. Berlin: Springer-Verlag. Lect. Notes Math. 1557, 86-96 (1993). Reviewer: S.Goldstein (Łódź) MSC: 46L51 46L53 46L54 46L60 15A66 81S10 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Lasenby, Anthony; Doran, Chris; Gull, Stephen Grassmann calculus, pseudoclassical mechanics, and geometric algebra. (English) Zbl 0812.58011 J. Math. Phys. 34, No. 8, 3683-3712 (1993). Reviewer: V.Pestov (Wellington) MSC: 58C50 15A66 15A75 81S10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Thorbergsson, Gudlaugur Clifford algebras and polar planes. (English) Zbl 0765.51015 Duke Math. J. 67, No. 3, 627-632 (1992). Reviewer: D.Ferus (Berlin) MSC: 51H15 15A66 51A50 51E24 × Cite Format Result Cite Review PDF Full Text: DOI
Oziewicz, Z.; Sitarczyk, Cz. Parallel treatment of Riemannian and symplectic Clifford algebras. (English) Zbl 0765.15019 Clifford algebras and their applications in mathematical physics, Proc. 2nd Workshop, Montpellier/Fr. 1989, Fundam. Theor. Phys. 47, 83-95 (1992). Reviewer: N.D.Sengupta (Bombay) MSC: 15A66 17B37 81R50 × Cite Format Result Cite Review PDF
Robinson, P. L. Pure symplectic spinors in the Fock representation. (English) Zbl 0799.22013 J. Lond. Math. Soc., II. Ser. 46, No. 2, 250-268 (1992). Reviewer: G.Roepstorff (Aachen) MSC: 22E70 81S10 53D50 22E45 × Cite Format Result Cite Review PDF Full Text: DOI
Salamon, Simon Special structures on four-manifolds. (English) Zbl 0796.53031 Riv. Mat. Univ. Parma, IV. Ser. 17*, 109-123 (1991). Reviewer: C.-L.Tiba (Iaşi) MSC: 53C15 × Cite Format Result Cite Review PDF
Crumeyrolle, Albert Orthogonal and symplectic Clifford algebras. Spinor structures. (English) Zbl 0701.53003 Mathematics and Its Applications, 57. Dordrecht etc.: Kluwer Academic Publishers Group. xiii, 350 p. Dfl. 240.00; £79.00; $ 124.00 (1990). Reviewer: Joseph D. Zund (Las Cruces) MSC: 53-02 53C27 15A90 53B50 53C15 15A66 15-02 × Cite Format Result Cite Review PDF
Kostrikin, A. I.; Manin, Yu. I. Linear algebra and geometry. Transl. from the 2nd Russian edition by M. E. Alferieff. (English) Zbl 0755.15002 Algebra, Logic and Applications. 1. New York etc.: Gordon & Breach Science Publishers. ix, 309 pp. (1989). MSC: 15-01 15A63 51N10 51N15 15A69 81Q10 81S10 11E81 15A66 53B35 15A03 × Cite Format Result Cite Review PDF
Robinson, P. L.; Rawnsley, J. H. The metaplectic representation, \(\text{Mp}^ c\) structures and geometric quantization. (English) Zbl 0681.22022 Mem. Am. Math. Soc. 410, 92 p. (1989). MSC: 22E70 53D50 81S10 53C10 × Cite Format Result Cite Review PDF Full Text: DOI
Chisholm, J. S. R. Complex Clifford algebra formulation of Hamiltonian theory. (English) Zbl 0667.70019 Simon Stevin 62, No. 3-4, 201-207 (1988). MSC: 70H05 37J99 15A66 70G45 × Cite Format Result Cite Review PDF
Crumeyrolle, A. Planck’s constant and symplectic geometry. (English) Zbl 0645.58021 Topics in differential geometry, Pap. Colloq., Hajduszoboszló/Hung. 1984, Vol. 1, Colloq. Math. Soc. János Bolyai 46, 277-297 (1988). Reviewer: A.Bacciotti MSC: 37J99 15A66 53C80 81T99 17B65 × Cite Format Result Cite Review PDF