# Chaotic decompositions in ${\mathbb{Z}}_{2}$-graded quantum stochastic calculus

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 167-174
- ISSN: 0137-6934

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topEyre, Timothy. "Chaotic decompositions in $ℤ_2$-graded quantum stochastic calculus." Banach Center Publications 43.1 (1998): 167-174. <http://eudml.org/doc/208835>.

@article{Eyre1998,

abstract = {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.},

author = {Eyre, Timothy},

journal = {Banach Center Publications},

keywords = {-graded quantum stochastic calculus; superalgebraic structure; space of iterated integrals; chaotic expansions of polynomials},

language = {eng},

number = {1},

pages = {167-174},

title = {Chaotic decompositions in $ℤ_2$-graded quantum stochastic calculus},

url = {http://eudml.org/doc/208835},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Eyre, Timothy

TI - Chaotic decompositions in $ℤ_2$-graded quantum stochastic calculus

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 167

EP - 174

AB - 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.

LA - eng

KW - -graded quantum stochastic calculus; superalgebraic structure; space of iterated integrals; chaotic expansions of polynomials

UR - http://eudml.org/doc/208835

ER -

## References

top- [C] C. Chevalley, The Construction and Study of Certain Important Algebras, Publ. Math. Soc. Japan I, Princeton University Press, Princeton, NJ, 1955. Zbl0065.01901
- [E1] T. M. W. Eyre, Chaotic Expansions of Elements of the Universal Enveloping Superalgebra Associated with a ${\mathbb{Z}}_{2}$-Graded Quantum Stochastic Calculus, Commun. Math. Phys. 192 (1998), 9-28. Zbl0910.60094
- [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. Zbl0882.60097
- [HP1] R. L. Hudson and K. R. Parthasarathy, Quantum Ito's Formula and Stochastic Evolutions, Commun. Math. Phys. 93 (1984), 301-323. Zbl0546.60058
- [HP2] R. L. Hudson and K. R. Parthasarathy, Unification of Fermion and Boson Stochastic Calculus, Commun. Math. Phys. 104 (1986), 457-470. Zbl0604.60063
- [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. Zbl0904.60084
- [K] V. G. Kac, Lie Superalgebras, Advances in Mathematics 26 (1977), 8-96. Zbl0366.17012
- [L] J. M. Lindsay, Independence for Quantum Stochastic Integrators, Quantum Probability and Related Topics Vol. VI, 1991, 325-332. Zbl0937.60046
- [P] K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Birkhäuser, Basel (1992). Zbl0751.60046
- [S] M. Scheunert, The Theory of Lie Superalgebras, Lecture Notes in Mathematics, Vol. 716, Springer, Berlin, (1979). Zbl0407.17001

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