Kinematical Theory of Spinning Particles: Classical and Quantum Mechanical Formalism of Elementary Particles

Portada
Springer Science & Business Media, 30 nov. 2001 - 337 páginas
Classical spin is described in terms of velocities and acceleration so that knowledge of advanced mathematics is not required. Written in the three-dimensional notation of vector calculus, it can be followed by undergraduate physics students, although some notions of Lagrangian dynamics and group theory are required. It is intended as a general course at a postgraduate level for all-purpose physicists.
This book presents a unified approach to classical and quantum mechanics of spinning particles, with symmetry principles as the starting point.
A classical concept of an elementary particle is presented. The variational statements to deal with spinning particles are revisited. It is shown that, by explicitly constructing different models, symmetry principles are sufficient for the description of either classical or quantum-mechanical elementary particles. Several spin effects are analyzed.
 

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Índice

GENERAL FORMALISM
1
11 KINEMATICS AND DYNAMICS
3
2 VARIATIONAL VERSUS NEWTONIAN FORMALISM
4
3 GENERALIZED LAGRANGIAN FORMALISM
8
4 KINEMATICAL VARIABLES
10
41 EXAMPLES
16
5 CANONICAL FORMALISM
17
6 LIE GROUPS OF TRANSFORMATIONS
19
1 FEYNMANS QUANTIZATION OF LAGRANGIAN SYSTEMS
170
11 REPRESENTATION OF OBSERVABLES
173
2 NONRELATIVISTIC PARTICLES
177
22 NONRELATIVISTIC SPINNING PARTICLES BOSONS
179
23 NONRELATIVISTIC SPINNING PARTICLES FERMIONS
182
24 GENERAL NONRELATIVISTIC SPINNING PARTICLE
184
3 SPINORS
185
31 SPINOR REPRESENTATION ON SU2
189

61 CASIMIR OPERATORS
23
63 HOMOGENEOUS SPACE OF A GROUP
25
7 GENERALIZED NOETHERS THEOREM
26
8 LAGRANGIAN GAUGE FUNCTIONS
31
9 RELATIVITY PRINCIPLE KINEMATICAL GROUPS
33
10 ELEMENTARY SYSTEMS
34
101 ELEMENTARY LAGRANGIAN SYSTEMS
39
SIMPLEST KINEMATICAL GROUPS
40
NONRELATIVISTIC ELEMENTARY PARTICLES
47
1 GALILEI GROUP
48
2 NONRELATIVISTIC POINT PARTICLE
51
3 GALILEI SPINNING PARTICLES
55
4 GALILEI FREE PARTICLE WITH ANTI ORBITAL SPIN
63
41 INTERACTING WITH AN EXTERNAL ELECTROMAGNETIC FIELD
67
42 CANONICAL ANALYSIS OF THE SYSTEM
69
43 SPINNING PARTICLE IN A UNIFORM MAGNETIC FIELD
72
44 SPINNING PARTICLE IN A UNIFORM ELECTRIC FIELD
84
45 CIRCULAR ZITTERBEWEGUNG
85
5 SPINNING GALILEI PARTICLE WITH ORIENTATION
86
6 GENERAL NONRELATIVISTIC SPINNING PARTICLE
87
61 CIRCULAR ZITTERBEWEGUNG
90
62 CLASSICAL NONRELATIVISTIC GYROMAGNETIC RATIO
92
7 INTERACTION WITH AN EXTERNAL FIELD
93
8 TWOPARTICLE SYSTEMS
98
81 SYNCHRONOUS DESCRIPTION
99
9 TWO INTERACTING SPINNING PARTICLES
103
RELATIVISTIC ELEMENTARY PARTICLES
109
1 POINCARE GROUP
110
11 LORENTZ GROUP
113
2 RELATIVISTIC POINT PARTICLE
118
3 RELATIVISTIC SPINNING PARTICLES
121
32 RELATIVISTIC PARTICLES WITH ANTI ORBITAL SPIN
137
33 CANONICAL ANALYSIS
142
34 CIRCULAR ZITTERBEWEGUNG
145
4 LUXONS
147
41 MASSLESS PARTICLES THE PHOTON
148
42 MASSIVE PARTICLES THE ELECTRON
151
5 TACHYONS
160
6 INVERSIONS
162
7 INTERACTION WITH AN EXTERNAL FIELD
163
QUANTIZATION OF LAGRANGIAN SYSTEMS
169
32 MATRIX REPRESENTATION OF INTERNAL OBSERVABLES
196
34 GENERAL SPINORS
200
4 RELATIVISTIC PARTICLES
203
42 GENERAL RELATIVISTIC SPINNING PARTICLE
204
43 DIRACS EQUATION
206
44 DIRACS ALGEBRA
215
45 PHOTON QUANTIZATION
217
46 QUANTIZATION OF TACHYONS
218
OTHER SPINNING PARTICLE MODELS
221
12 KIRILLOVKOSTANTSOURIAU MODEL
225
13 BILOCAL MODEL
228
2 NONGROUP BASED MODELS
232
22 WEYSSENHOFFRAABE MODEL
234
23 BHABHACORBEN MODEL
240
24 BARGMANNMICHELTELEGDI MODEL
243
25 BARUTZANGHI MODEL
245
26 ENTRALGOKURYSHKIN MODEL
248
SPIN FEATURES AND RELATED EFFECTS
253
1 ELECTROMAGNETIC STRUCTURE OF THE ELECTRON
254
12 GYROMAGNETIC RATIO
264
13 INSTANTANEOUS ELECTRIC DIPOLE
266
14 DARWIN TERM OF DIRACS HAMILTONIAN
270
21 SPIN POLARIZED TUNNELING
278
3 QUANTUM MECHANICAL POSITION OPERATOR
279
4 FINSLER STRUCTURE OF KINEMATICAL SPACE
285
41 PROPERTIES OF THE METRIC
287
42 GEODESICS ON FINSLER SPACE
288
43 EXAMPLES
290
5 EXTENDING THE KINEMATICAL GROUP
291
51 SPACETIME DILATIONS
292
52 LOCAL ROTATIONS
293
53 LOCAL LORENTZ TRANSFORMATIONS
294
6 CONFORMAL INVARIANCE
295
62 CONFORMAL GROUP OF MINKOWSKI SPACE
298
63 CONFORMAL OBSERVABLES OF THE PHOTON
304
64 CONFORMAL OBSERVABLES OF THE ELECTRON
305
7 CLASSICAL LIMIT OF QUANTUM MECHANICS
306
Epilogue
311
References
315
Index
329
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Pasajes populares

Página 309 - Adler, in Lectures on Elementary Particles and Quantum Field Theory, edited by S. Deser, M. Grisaru, and H. Pendleton (MIT Press, Cambridge, Mass., 1970).
Página 251 - V. Bargmann, L. Michel, and VL Telegdi, Phys. Rev. Lett. 2 435 (1959) 11.

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