Chaotic decompositions in $ℤ_2$-graded quantum stochastic calculus

• Autorzy: Timothy M. W. Eyre
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 43
• Numer: 1
• Strony: 167-174

Daty

wydano

1998

Twórcy

autor

Timothy M. W. Eyre

• 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).