کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
838903 908374 2007 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
(Co)bordism groups in quantum super PDEs. II: Quantum super PDEs
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
(Co)bordism groups in quantum super PDEs. II: Quantum super PDEs
چکیده انگلیسی

Following our previous works on the integral (co)bordism groups of quantum PDEs [A. Prástaro, Geometry of PDEs and Mechanics, World Scientific Publishing Co., Singapore, 1996, 760pp; A. Prástaro, (Co)bordisms in PDE's and quantum PDE's, Rep. Math. Phys. 38(3) (1996) 443–455; A. Prástaro, Quantum and integral (co)bordism groups in partial differential equations, Acta Appl. Math. 51(3) (1998) 243–302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59(2) (1999) 111–202; A. Prástaro, (Co)bordism groups in quantum PDE's, Acta Appl. Math. 64(2/3) (2000) 111–217; A. Prástaro, Quantum manifolds and integral (co)bordism groups in quantum partial differential equations, Nonlinear Anal. 47/4 (2001) 2609–2620; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co., Singapore, 2004, 500pp; A. Prástaro, Quantum super Yang-Mills equations: global existence and mass-gap, Dynamic Syst. Appl. 4 (2004) 227–234; A. Prástaro, Th.M. Rassias, A geometric approach to a noncommutative generalized d’Alembert equation, C. R. Acad. Sci. Paris 330(I-7) (2000) 545–550; A. Prástaro, Th.M. Rassias, Results on the J.D’Alembert equation, Ann Acad. Paed. Crac. Stud. Math. 1 (2001) 117–128.], we specialize, now, on quantum super partial differential equations, i.e., partial differential equations built in the category of quantum supermanifolds  . These are manifolds modeled on locally convex topological vector spaces built starting from quantum algebras endowed also with a Z2Z2-gradiation, and a Z2Z2-graded Lie algebra structure, (quantum superalgebra). Then, we extend to these manifolds, with such richer structure, our previous results, and build a geometric theory of quantum super PDEs, that allows us to obtain theorems of existence of (smooth) local and global solutions in the category of quantum supermanifolds. Some quantum (super) PDEs, arising from the Dirac quantization of some classical (super) PDEs, are considered in some details.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Real World Applications - Volume 8, Issue 2, April 2007, Pages 480–504
نویسندگان
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