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preface
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1��special relativity
��1.1   introduction
��1.2  the principles of special relativity
��1.3  transformation of coordinates and velocities
����1.3.1  lorentz transformation
����1.3.2  transformation of velocities
����1.3.3  lorentz boost in an arbitrary direction
��1.4  four-vectors
����1.4.1  four-velocity and acceleration
��1.5  tensors
��1.6  tensors as geometrical objects
��1.7  volume and surface integrals in four dimensions
��1.8  particle dynamics
��1.9  the distribution function and its moments
��1.10 the lorentz group and pauli matrices
2��scalar and electromagnetic fields in special relativity
��2.1  introduction
��2.2  external fields of force
��2.3  classical scalar field
����2.3.1  dynamics of a particle interacting with a scalarfield
����2.3.2  action and dynamics of the scalar field
����2.3.3  energy-momentum tensor for the scalar field
����2.3.4  free field and the wave solutions
����2.3.5  why does the scalar field lead to an attractiveforce?
��2.4  electromagnetic field
����2.4.1  charged particle in an electromagnetic field
����2.4.2  lorentz transformation of electric and magneticfields
����2.4.3  current vector
��2.5   motion in the coulomb field
��2.6  motion in a constant electric field
��2.7  action principle for the vector field
��2.8   maxwell's equations
��2.9  energy and momentum of the electromagnetic field
��2.10 radiation from an accelerated charge
��2.11  larmor formula and radiation reaction
3��gravity and spaeetime geometry: the inescapable connection
��3.1   introduction
��3.2  field theoretic approaches to gravity
��3.3   gravity as a scalar field
��3.4   second rank tensor theory of gravity
��3.5   the principle of equivalence and the geometricaldescription��of gravity
���� 3.5.1  uniformly accelerated observer
���� 3.5.2  gravity and the flow of time
4��metric tensor, geodesics and covariant derivative
�� 4.1   introduction
�� 4.2  metric tensor and gravity
�� 4.3   tensor algebra in curved spacetime
�� 4.4  volume and surface integrals
�� 4.5   geodesic curves
���� 4.5.1  properties of geodesic curves
���� 4.5.2  affine parameter and null geodesics
�� 4.6  covariant derivative
���� 4.6.1  geometrical interpretation of the covariantderivative
���� 4.6.2  manipulation of covariant derivatives
�� 4.7   parallel transport
�� 4.8   lie transport and killing vectors
�� 4.9   fermi-walker transport
5��curvature of spaeetime
�� 5.1   introduction
�� 5.2   three perspectives on the spacetimecurvature
���� 5.2.1  parallel transport around a closed curve
���� 5.2.2  non-commutativity of covariant derivatives
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