Contains:
1. GENERAL FORMALISM

1 . Introduction

1.1

Kinematics and dynamics

2 . Variational versus Newtonian formalism

3 . Generalized Lagrangian formalism

4 . Kinematical variables

4.1

Examples

5 . Canonical formalism

6 . Lie groups of transformations

6.1

Casimir operators

6.2

Exponents of a group

6.3

Homogeneous space of a group

7 . Generalized Noether’s theorem

8 . Lagrangian gauge functions

9 . Relativity principle. Kinematical groups

10 . Elementary systems

10.1

Elementary Lagrangian systems

11 . The formalism with the simplest kinematical groups

2. NONRELATIVISTIC


ELEMENTARY PARTICLES

1 . Galilei group

2 . Nonrelativistic point particle

3 . Galilei spinning particles

4 . Galilei free particle with (anti)orbital spin

4.1

Interacting with an external electromagnetic field

4.2

Canonical analysis of the system

vii

viii


KINEMATICAL THEORY OF SPINNING PARTICLES


Spinning particle in a uniform magnetic field


4.3

Spinning particle in a uniform electric field

4.4

4.5

Circular zitterbewegung

Spinning Galilei particle with orientation

General nonrelativistic spinning particle

6.1

Circular zitterbewegung

6.2

Classical nonrelativistic gyromagnetic ratio

Interaction with an external field

Twoparticle systems

8.1

Synchronous description

Two interacting spinning particles

5.


6.


7.

8.

9.


3. RELATIVISTIC


ELEMENTARY PARTICLES

1 . PoincarÃ© group

1.1

Lorentz group

2 . Relativistic point particle

3 . Relativistic spinning particles

3.1

Bradyons

3.2

Relativistic particles with (anti)orbital spin

3.3

Canonical analysis

3.4

Circular zitterbewegung

4 . Luxons

4.1

Massless particles. (The photon)

4.2

Massive particles. (The electron)

5 . Tachyons

6 . Inversions

7 . Interaction with an external field

4. QUANTIZATION OF


LAGRANGIAN SYSTEMS

1 . Feynman’s quantization of Lagrangian systems

1.1

Representation of Observables

2 . Nonrelativistic particles

2.1

Nonrelativistic point particle

2.2

Nonrelativistic spinning particles. Bosons

2.3

Nonrelativistic spinning particles. Fermions

2.4

General nonrelativistic spinning particle

3. Spinors

3.1

Spinor representation on SU(2)

3.2

Matrix representation of internal observables

3.3

PeterWeyl theorem for compact groups

3.4

General spinors

4 . Relativistic particles

4.1

Relativistic point particle

4.2

General relativistic spinning particle

4.3

Dirac’s equation


Contents i x


4.4

4.5

4.6


5. OTHER SPINNING PARTICLE

MODELS

1 . Group theoretical models

1.1

Hanson and Regge spinning top

1.2

KirillovKostantSouriau model

Bilocal model

1.3

2 . Nongroup based models

2.1

Spherically symmetric rigid body

2.2

WeyssenhoffRaabe model

BhabhaCorben model

2.3

2.4

BargmannMichelTelegdi model

BarutZanghi model

2.5

EntralgoKuryshkin model

2.6

6. SPIN FEATURES


AND RELATED EFFECTS

1 . Electromagnetic structure of the electron

The time average electric and magnetic field

1.1

1.2

Gyromagnetic ratio

Instantaneous electric dipole

1.3

1.4

Darwin term of Dirac’s Hamiltonian

2 . Classical spin contribution to the tunnel effect

2.1

Spin polarized tunneling

3 . Quantum mechanical position operator

4 . Finsler structure of kinematical space

4.1

Properties of the metric

4.2

Geodesics on Finsler space

Examples

4.3

5 . Extending the kinematical group

Spacetime dilations

5.1

Local rotations

5.2

Local Lorentz transformations

5.3

6 . Conformal invariance

Conformal group

6.1

Conformal group of Minkowski space

6.2

Conformal observables of the photon

6.3

Conformal observables of the electron

6.4

7 . Classical Limit of quantum mechanics

Dirac’s algebra


Photon quantization

Quantization of tachyons

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