Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
A brief introduction to $ℤ_2$-graded quantum stochastic calculus is given. By inducing a superalgebraic structure on the space of iterated integrals and using the heuristic classical relation df(Λ) = f(Λ + dΛ) - f(Λ) we provide an explicit formula for chaotic expansions of polynomials of the integrator processes of $ℤ_2$-graded quantum stochastic calculus.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
167-174
Opis fizyczny
Daty
wydano
1998
Twórcy
autor
- Department of Mathematics, University of Nottingham, Nottingham, NG7 2RD, UK
Bibliografia
- [C] C. Chevalley, The Construction and Study of Certain Important Algebras, Publ. Math. Soc. Japan I, Princeton University Press, Princeton, NJ, 1955.
- [E1] T. M. W. Eyre, Chaotic Expansions of Elements of the Universal Enveloping Superalgebra Associated with a $ℤ_2$-Graded Quantum Stochastic Calculus, Commun. Math. Phys. 192 (1998), 9-28.
- [E2] T. M. W. Eyre, Graded Quantum Stochastic Calculus and Representations of Lie Superalgebras, Lecture Notes in Mathematics, Springer, Berlin, to appear; earlier form exists as Nottingham preprint.
- [EH] T. M. W. Eyre and R. L. Hudson, Representations of Lie Superalgebras and Generalised Boson-Fermion Equivalence in Quantum Stochastic Calculus, Commun. Math. Phys. 186 (1997), 87-94.
- [HP1] R. L. Hudson and K. R. Parthasarathy, Quantum Ito's Formula and Stochastic Evolutions, Commun. Math. Phys. 93 (1984), 301-323.
- [HP2] R. L. Hudson and K. R. Parthasarathy, Unification of Fermion and Boson Stochastic Calculus, Commun. Math. Phys. 104 (1986), 457-470.
- [HPu] R. L. Hudson and S. Pulmannova, Chaotic Expansions of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus, Proc. LMS, to appear.
- [K] V. G. Kac, Lie Superalgebras, Advances in Mathematics 26 (1977), 8-96.
- [L] J. M. Lindsay, Independence for Quantum Stochastic Integrators, Quantum Probability and Related Topics Vol. VI, 1991, 325-332.
- [P] K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Birkhäuser, Basel (1992).
- [S] M. Scheunert, The Theory of Lie Superalgebras, Lecture Notes in Mathematics, Vol. 716, Springer, Berlin, (1979).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv43i1p167bwm