Math 257A: Introduction to Symplectic Topology, Lecture 2
... (M ) ∼ = R. Definition 1. If ω is exact and symplectic then (M, ω) is called an exact symplectic manifold. Note. If (M, ω) is exact then M cannot be closed (i.e. compact without boundary). Non-example 3. The spheres S 2n for n ≥ 2 are not symplectic because H 2 (S 2n ) = 0. Definition 2. A diffeomor ...
... (M ) ∼ = R. Definition 1. If ω is exact and symplectic then (M, ω) is called an exact symplectic manifold. Note. If (M, ω) is exact then M cannot be closed (i.e. compact without boundary). Non-example 3. The spheres S 2n for n ≥ 2 are not symplectic because H 2 (S 2n ) = 0. Definition 2. A diffeomor ...
An Introduction to Unitary Representations of Lie Groups
... infinite measure. Therefore the representation (π, H) contains no irreducible subspaces and we need refined methods to say what it means to decompose it into irreducible ones. The problem of decomposing functions into simpler pieces with respect to the transformation behavior under a certain symmetr ...
... infinite measure. Therefore the representation (π, H) contains no irreducible subspaces and we need refined methods to say what it means to decompose it into irreducible ones. The problem of decomposing functions into simpler pieces with respect to the transformation behavior under a certain symmetr ...
Maximizing the entanglement of two mixed qubits
... how can one increase its linear entropy given a certain degree of entanglement? It was shown by Lewenstein and Sanpera 关26兴 that any two-qubit entangled state can be written as a mixture of a separable state and a single pure entangled state. The Werner state 共4兲 is recognizably of this form. All it ...
... how can one increase its linear entropy given a certain degree of entanglement? It was shown by Lewenstein and Sanpera 关26兴 that any two-qubit entangled state can be written as a mixture of a separable state and a single pure entangled state. The Werner state 共4兲 is recognizably of this form. All it ...
Aspects of quantum information theory
... this end the text is divided into two parts. The first (Part I. “Fundamentals”) is of introductory nature. It takes into account that most of the fundamental concepts and basic ideas of quantum information are developed during the last decade, and are therefore unfamiliar to most physicists. To make ...
... this end the text is divided into two parts. The first (Part I. “Fundamentals”) is of introductory nature. It takes into account that most of the fundamental concepts and basic ideas of quantum information are developed during the last decade, and are therefore unfamiliar to most physicists. To make ...
ROOT NUMBERS OF HYPERELLIPTIC CURVES 1. Introduction
... subgroup C of W 0 (K/K) is complex analytic. It is known that there is a bijection between representations of W 0 (K/K) and pairs (σ, N ), where σ : W(K/K) −→ GL(U ) is a continuous complex representation of W(K/K) and N is a nilpotent endomorphism on U such that σ(g)N σ(g)−1 = ω(g)N, g ∈ W(K/K). In ...
... subgroup C of W 0 (K/K) is complex analytic. It is known that there is a bijection between representations of W 0 (K/K) and pairs (σ, N ), where σ : W(K/K) −→ GL(U ) is a continuous complex representation of W(K/K) and N is a nilpotent endomorphism on U such that σ(g)N σ(g)−1 = ω(g)N, g ∈ W(K/K). In ...
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... count how many times each set of labels appears and label states by these numbers: ...
... count how many times each set of labels appears and label states by these numbers: ...
