| Preface | p. xi |
| Dirac Observables and [psi]do-s | p. 1 |
| Introduction | p. 1 |
| Some Special Distributions | p. 10 |
| Strictly Classical Pseudodifferential Operators | p. 14 |
| Ellipticity and Parametrix Construction | p. 18 |
| L[superscript 2]-Boundedness and Weighted Sobolev Spaces | p. 20 |
| The Parametrix Method for Solving ODE-s | p. 26 |
| More on General [psi]do-Results | p. 31 |
| Why Should Observables be Pseudodifferential? | p. 37 |
| Introduction | p. 37 |
| Smoothness of Lie Group Action on [psi]do-s | p. 39 |
| Rotation and Dilation Smoothness | p. 42 |
| General Order and General H[subscript s]-Spaces | p. 46 |
| A Useful Result on L[superscript 2]-Inverses and Square Roots | p. 50 |
| Decoupling with [psi]do-s | p. 55 |
| Introduction | p. 55 |
| The Foldy-Wouthuysen Transform | p. 59 |
| Unitary Decoupling Modulo O(-[infinity]) | p. 61 |
| Relation to Smoothness of the Heisenberg Transform | p. 65 |
| Some Comments Regarding Spectral Theory | p. 67 |
| Complete Decoupling for V(x) [nequiv] | p. 70 |
| Split and Decoupling are not unique - Summary | p. 76 |
| Decoupling for Time Dependent Potentials | p. 78 |
| Smooth Pseudodifferential Heisenberg Representation | p. 83 |
| Introduction | p. 83 |
| Dirac Evolution with Time-Dependent Potentials | p. 85 |
| Observables with Smooth Heisenberg Representation | p. 88 |
| Dynamical Observables with Scalar Symbol | p. 96 |
| Symbols Non-Scalar on S[plus or minus] | p. 101 |
| Spin and Current | p. 106 |
| Classical Orbits for Particle and Spin | p. 110 |
| The Algebra of Precisely Predictable Observables | p. 117 |
| Introduction | p. 117 |
| A Precise Result on [psi]do-Heisenberg Transforms | p. 119 |
| Relations between the Algebras P(t) | p. 125 |
| About Prediction of Observables again | p. 127 |
| Symbol Propagation along Flows | p. 128 |
| The Particle Flows Components are Symbols | p. 132 |
| A Secondary Correction for the Electrostatic Potential | p. 137 |
| Smoothness and FW-Decoupling | p. 142 |
| The Final Algebra of Precisely Predictables | p. 147 |
| Lorentz Covariance of Precise Predictability | p. 149 |
| Introduction | p. 149 |
| A New Time Frame for a Dirac State | p. 156 |
| Transformation of P and PX for Vanishing Fields | p. 160 |
| Relating Hilbert Spaces; Evolution of the Spaces H[prime] and H | p. 168 |
| The General Time-Independent Case | p. 171 |
| The Fourier Integral Operators around R | p. 175 |
| Decoupling with Respect to H[prime] and H(t) | p. 180 |
| A Complicated ODE with [psi]do-Coefficients | p. 183 |
| Integral Kernels of e[superscript i | p. 187 |
| Spectral Theory of Precisely Predictable Approximations | p. 193 |
| Introduction | p. 193 |
| A Second Order Model Problem | p. 195 |
| The Corrected Location Observable | p. 199 |
| Electrostatic Potential and Relativistic Mass | p. 202 |
| Separation of Variables in Spherical Coordinates | p. 206 |
| Highlights of the Proof of Theorem 7.3.2 | p. 216 |
| The Regular Singularities | p. 222 |
| The Regular Singularity at 0 | p. 222 |
| The Regular Singularity at r = 1/[lambda] | p. 223 |
| The Singularity at [infinity] | p. 224 |
| Asymptotic Behaviour of Solutions at Infinity | p. 224 |
| The Asymptotic Expansion at [infinity]; Dependence on [lambda] | p. 229 |
| Final Arguments | p. 230 |
| Fitting Together our Wave Distributions | p. 230 |
| Final Construction of the Distribution Kernel U(r, p) of (7.3.11) | p. 233 |
| About the Negative Spectrum | p. 234 |
| Final Comments | p. 234 |
| Dirac and Schrodinger Equations; a Comparison | p. 237 |
| Introduction | p. 237 |
| What is a C[superscript *]-Algebra with Symbol? | p. 241 |
| Exponential Actions on A | p. 243 |
| Strictly Classical Pseudodifferential Operators | p. 245 |
| Characteristic Flow and Particle Flow | p. 249 |
| The Harmonic Oscillator | p. 252 |
| References | p. 259 |
| General Notations | p. 263 |
| Index | p. 265 |
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