引力场中的量子信息--聚文网

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内容简介

本书提供了对爱因斯坦广义相对论所描述的经典引力场下的量子信息的简要讨论。除了对弯曲时空中量子场的基本物理原理进行基本描述外，本书还提供了一些有关惯性坐标系中隐写量子通信、史瓦西时空中的量子位，史瓦西时空中的自旋曲率耦合、克尔时空中的量子位以及引力场中量子技术的性能的新结果。

Preface
Acknowledgements
Biography
1 Introduction
1.1 Quantum information
1.2 Quantum communications
1.3 Quantum computing
1.4 Quantum sensors
1.5 Relativistic quantum information
1.6 Summary
2 Special and general relativity
2.1 Special relativity
2.2 Lorentz transformations
2.3 Lagrangian dynamics
2.4 The principle of equivalence
2.4.1 Particle dynamics in a gravitational field
2.4.2 Torsion
2.4.3 Geodesics and geodesic congruences
2.5 The principle of general covariance
2.5.1 Tensor analysis
2.5.2 Covariant derivatives
2.5.3 The coordinate basis
2.5.4 The minimal substitution rule
2.5.5 The energy-momentum tensor
2.5.6 The Euler-Lagrange equations
2.6 The Hamilton-Jacobi equations
2.7 Einstein's field equations
2.8 Principles of conservation
2.9 Killing vectors
2.10 Tetrad fields
2.11 Spin in general relativity
2.12 The spin-curvature coupling
2.13 Summary
3 Relativistic quantum fields
3.1 The Schrodinger equation
3.2 The Klein-Gordon equation
3.3 Scalar quantum fields
3.4 The quantum Poincare transformations
3.5 Wigner rotations
3.5.1 Massive particles
3.5.2 Massless particles
3.6 The Dirac equation
3.6.1 SO(3) and SU(2)
3.6.2 SL(2,C) and SO+(3,1)
3.6.3 Four-spinors
3.6.4 Particle dynamics
3.6.5 Free particle spinors
3.6.6 Spin and helicity
3.7 Dirac quantum fields
3.8 Group representations in quantum field theory
3.8.1 Non-unitary representations of the Lorentz group and quantum fields
3.8.2 Unitary representations of the Poincare group and quantum states
3.8.3 Unitary/non-unitary representations and wave functions
3.9 Representations of quantum fields with arbitrary spin
3.9.1 Scalar fields
3.9.2 Vector fields
3.9.3 Tensor fields
3.9.4 Dirac fields
3.10 The quantum vacuum in flat spacetime
3.11 Summary
4 Quantum information in inertial frames
4.1 Qubit transformations
4.2 Relativistic dynamics
4.3 Steganographic quantum channel
4.3.1 Relativistic communications
4.3.2 Relativistic fixed points
4.4 The teleportation channel
4.4.1 Relativistic teleportation
4.4.2 Absence of relativistic fixed points
4.5 Spread momentum states
4.6 Summary
5 Quantum fields in curved spaeetimes
5.1 Scalar fields in curved spacetime
5.2 Quantum dynamics in general relativity
5.2.1 The plane wave approximation
5.2.2 Hilbert spaces
5.2.3 Scalar orbital angular momentum eigenstates
5.2.4 Scalar four-momentum eigenstates
5.3 The quantum vacuum in a gravitational field
5.4 The spin-statistics connection
5.5 Quantum vector fields in curved spacetime
5.6 Spinors in curved spacetimes
5.7 Covariant derivative for fields of arbitrary spin
5.7.1 General form
5.7.2 Scalar fields
5.7.3 Vector fields
5.7.4 Tetrad fields
5.7.5 Dirac fields
5.8 Spinor dynamics with tetrad fields
5.9 Dirac spinors in curved spacetime
5.9.1 Solution at order h
5.9.2 Geodesic deviation at order h1
5.10 The spin-curvature coupling
5.11 Summary
6 Qubits in Schwarzschild spacetime
6.1 Metric tensor
6.2 Structure of Schwarzschild spacetime
6.3 Tetrad fields and connection one-forms
6.3.1 Affine connections
6.3.2 Curvature tensor
6.3.3 Tetrad fields
6.3.4 Connection one-forms
6.4 Geodesics
6.5 Quantum dynamics
6.6 Wigner rotations
6.6.1 Equatorial radial fall (θ = π/2, J = O)
6.6.2 Equatorial circular orbits (θ = π/2, ur = 0)
6.6.3 General equatorial circular paths (θ = π/2, ar≠0)
6.6.4 Geodetic precession of classical gyroscopes
6.7 Radiation damping
6.8 Summary
7 Spin-curvature coupling in Schwarzschild spacetime
7.1 Spinor components
……

引力场中的量子信息

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