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Schurmann M. — White Noise on Bialgebras
Schurmann M. — White Noise on Bialgebras

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Название: White Noise on Bialgebras

Автор: Schurmann M.

Аннотация:

These notes are a contribution to the field of quantum (or non-commutative) probability theory. Quantum probability can be regarded as an attempt of a unified approach to classical probability and the quantum theory of irreversible processes.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 153

Добавлена в каталог: 19.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adapted process      57 58
Additive left white noise      85 88
Additive right white noise      85 88
Additive white noise      24
Algebra      12 15
Ampliation      46 81
Annihilation operator      109
Annihilation process      57 108
Anti-symmetric independence      17
Antipode      30
Araki — Woods embedding theorem      103
Azema martingale      81 93 137
Azema noise      94 137
Backward equation      84 85 89
Backward integral      68 84
Basic formula      52 53
Bialgebra      29 30
Bialgebra, $(\gamma, \alpha)$-      29
Bialgebra, cocommutative      103 112
Bialgebra, Graded      103
Bialgebra, involutive      30
Bialgebra, involutive $(\gamma, \alpha)$-      30
Bialgebra, symmetric      30
Bose Fock space      41
Bose independence      17
Bose quantum Brownian motion      94
Bose quantum Wiener process      92 94
Brownian motion, quantum      81 94 137
Canonical commutation relations      110
Central limit theorem      130
Coalgebra      12
Coalgebra stochastic integral equation      65
Coalgebra, cocommutative      29 104
Coalgebra, Graded      15 29
Coassociativity      12
Coboundary      55 115
Cocommutative bialgebra      103 112
Cocommutative coalgebra      29 104
Cocycle      55 115
Coefficient algebra      31
Coefficient algebra of matrix semi-group      31
Coefficient algebra, deformation of      32
Coefficient algebra, non-commutative analogue of      32
Coherent state      41
Commutation factor      19
Commutation factor, $\mathbb{L}-\mathbb{M}$-      19
Commutation rules      17
Comodule algebra      14
Comodule coalgebra      15
Comodule vector space      13
Comultiplication      12
Conditionally positive linear functional      36
Conditionally positive sesquilinear form      76
Convolution product of linear functionals      27
Convolution product of linear mappings      27
Convolution semi-group      36
Counit      12
Creation operator      109
Creation process      57 108
Deformation of Heisenberg group      34 73
Deformation of Lie algebra of SL(2)      35
Deformation of SU(2)      34
Derivation component      117
Derivation component, maximal      117
Differential second quantization      41 57
Differential second quantization operator      110
Distribution of a quantum random variable      16
Distribution, 1-dimensional      16
Double module *-algebra      15
Double module algebra      15
Double module coalgebra      15
Double module vector space      14
Embedding theorem      112
Enveloping Hopf algebra      31
Equivalent processes      16
Even element      14 104
Even linear functional      21 76
Exponential element      30
Exponential vector      41
Factorization property      17
Fermi Fock space      111
Fermi independence      17
Fermi quantum Brownian motion      94
Fermi quantum Wiener process      94
Fermi Wiener process      94
Fock space, Bose      41
Fock space, Fermi      111
Forward equation      84 85 89
Forward integral      68
Fundamental theorem on coalgebras      26 96
Gelfand — Naimark — Segal (GNS) construction      16
Gelfand — Naimark — Segal (GNS) representation      103 107 112
Gelfand — Naimark — Segal (GNS) triplet      90 112
Generator of white noise      37
GNS      see "Gelfand — Naimark — Segal"
Graded *-algebra      15
Graded *-vector space      15
Graded algebra      14
Graded coalgebra      15
Graded vector space      13
Graduation      21
Group      13
Group algebra      31 69
Group, involutive      15
Group-like element      30
Heisenberg group      32
Heisenberg group, deformation of      34 73
Hermitian linear functional      36
Hermitian operator      16
Hermitian sesquilinear form      76
Hochschildt cohomology      115
Homogeneous element      14
Hopf algebra      30
Hopf algebra, $(\gamma, \alpha)$-      30
Hopf algebra, enveloping      31
Hopf algebra, involutive      30
Hudson — Parthasarathy-integral      97 98
Independence      17
Independence, $(\gamma, \alpha)$-      18
Independence, anti-symmetric      17
Independence, left      18 21
Independence, right      19 21
Independence, symmetric      17
Infinitely divisible representation      113
Infinitely divisible state      111
Infinitesimal generator      37
Integral sum identity      43
Interpolation      94
Invariance principle      132
Invariant      22
Involutive bialgebra      30
Involutive group      15
Involutive vector space      15
Ito's formula      57 62
Kernel      45
Kernel integral      59
Kernel valued-process      57 58
Left independence      18 21
Left invariant derivation      116
Left white noise      72
Lie *-algebra      31 113
Lie element      30
Loqually square integrable process      97
Maassen kernel      41
Matrix *-bialgebra over a finite group      34
Maximal derivation component      117
Maximal quadratic component      118
Module algebra      14
Module coalgebra      15
Module vector space      13
Multiplicative white noise      25 73 94
Non-commutative coefficient algebra      32
Non-commutative Poisson process      92 122
Odd operator      110
Opposite bialgebra      30
Parity operator      18 104
Poisson process      81 92 101 122
Positive linear functional      15
Positive sesquilinear form      75
Preservation operator      110
Preservation process      81 108
Primitive element      30
Property (C')      119
Property (C)      119
Property (D)      119
Pyramidal ordering      37 38
Quadratic component      118
Quadratic component, maximal      118
Quadratic linear functional      114
Quadratic linear functional, degenerate      115
Quantum Brownian motion      81 94 137
Quantum Ito's formula      57 62
Quantum Poisson process      81 92 122
Quantum probability space      15
Quantum random matrix      24
Quantum random variable      16
Quantum random vector      23
Quantum stochastic differential equation      65 68
Quantum stochastic integral      58 59 62
Quantum stochastic process      16
Quantum white noise      35
Quantum Wiener process      92 94
Reconstruction theorem      40
Representation theorem for while noise, general case      84
Representation theorem for while noise, symmetric case      56 68
Representative function      26 94
Right independence      19 21
Right white noise      72
Schoenberg correspondence      74
Second quantization      82
Second quantization process      81 82 103
Semi-direct product      69
Semi-group      30
Semi-group algebra      30
State      15
Symmetric bialgebra      30
Symmetric independence      17
Symmetric white noise      73
Symmetrization      69
Tensor algebra      23 31
Tensor algebra, graded      24
Tensor algebra, involutive      24
Tensor Hopf algebra      31
Tensor product, $(\gamma, \alpha)$-      28
Tensor product, continuous      41
Tensor product, symmetric      41
Time-reversed white noise      38
Underlying additive white noise      88 103 130
Unitary group      25 32
Unitary q-white noise      25 101
Unitary white noise      25 99
VACUUM      54
Vector space      12
Vector space, $\mathbb{Z}_{2}$-graded      106
Vector space, graded      13
Vector space, involutive      15
Weyl algebra      123
White noise      35
White noise, $(\gamma, \alpha)$-      35
White noise, additive      24
White noise, left      72
White noise, multiplicative      25
White noise, quantum      35
White noise, right      72
White noise, unitary      25 99 101
Wiener process      91 101
Wiener process, Bose      92
Wiener process, Fermi      94
Wiener process, quantum      92 94
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