436
Index
Scattering (continued)
e
− μ
− , 254–257
lowest order, in ‘laboratory frame’,
256
e
− π
+ , elastic, 242–247
e
− -parton, 274–275
e
− -proton
Bjorken scaling in, 272–277
elastic, 8, 257–260
inelastic, 269–283
kinematics, 260–262
structure functions, 271–278
e
− s
+ , 234–242
+
μ
−
− → μ
+
e
+ e
, 247–250
e e
, 257, 265–266, 285
− → π
+ π
−
as exchange process, 15–20, 172–173
q¯ q → μμ ¯, 285
quasi-elastic, 275–276
Rutherford, see Rutherford scattering
theory,
non-relativistic, 399–403
time-dependent, 402–403
time-independent, 399–402
s-channel, 173, 249–250, 299
Schr¨ odinger equation for spinless particles, 49–51, 58–60, 63, 361
free-particle solutions, 361
and Galilean transformation, 111
interaction with electromagnetic
field, 49–61, 362
probability current density, 84, 361
probability density, 84, 361
Schr¨ odinger picture (formulation), 129,
153–155, 405–406
Sea, of negative-energy states, 76–77
Second quantization, 144
Self-energy
in ABC theory, 300–306, 314–318
renormalized, 322
fermion, in QED, 329–331
one-particle irreducible, 306
photon, in QED, 331–336
imaginary part of, 344–345
renormalized, 333–345
σ (Pauli) matrices, 68, 72, 85, 362
Slash notation, 110, 195
S-matrix, 156–158
Lorentz invariance of, 190
unitarity of, 156
ˆ
S-operator, 157–158
Dyson expansion of, 158
Lorentz invariance of, 166
Special relativity, 371–375
Spin matrices, 362
Spin-statistics connection, 191–195
Spin sums and projection operators, 408–
409
Spinor 68
conjugate, 110
four-component, 70
negative-energy, 75–76, 110
positive-energy, 74–75, 110
rest-frame, 72
and rotations, 89–92
self-conjugate (Majorana), 101–102,
212–213
two-component, 69, 72
and velocity transformations (boosts),
92–94
Spontaneously broken symmetry, 12, 15,
32
Standard Model, 3–4, 7, 41, 48, 61, 115,
146, 179, 299, 304, 343, 350–
352
Stokes’ theorem, 387
Strangeness, 9–10
conservation, 10, 35
Strange quark, 9–10
String theory, 4
Strong interactions, 26–29
Structure function, 271–272, 275–277
and positivity properties, 278
of proton, electromagnetic, 271–272
scaling of, 272–280
Subtraction, 323, 356
Sum rules, see Quark, parton model
Summation convention, 372
Super-renormalizable theory, 162, 318, 326,
353
Supersymmetry, 141
Symmetry
current, 186–187, 194, 207
internal, 57–58
operator, 184, 186–188, 194
Tau lepton, 5
and neutrino, 6
Index
Scattering (continued)
e
− μ
− , 254–257
lowest order, in ‘laboratory frame’,
256
e
− π
+ , elastic, 242–247
e
− -parton, 274–275
e
− -proton
Bjorken scaling in, 272–277
elastic, 8, 257–260
inelastic, 269–283
kinematics, 260–262
structure functions, 271–278
e
− s
+ , 234–242
+
μ
−
− → μ
+
e
+ e
, 247–250
e e
, 257, 265–266, 285
− → π
+ π
−
as exchange process, 15–20, 172–173
q¯ q → μμ ¯, 285
quasi-elastic, 275–276
Rutherford, see Rutherford scattering
theory,
non-relativistic, 399–403
time-dependent, 402–403
time-independent, 399–402
s-channel, 173, 249–250, 299
Schr¨ odinger equation for spinless particles, 49–51, 58–60, 63, 361
free-particle solutions, 361
and Galilean transformation, 111
interaction with electromagnetic
field, 49–61, 362
probability current density, 84, 361
probability density, 84, 361
Schr¨ odinger picture (formulation), 129,
153–155, 405–406
Sea, of negative-energy states, 76–77
Second quantization, 144
Self-energy
in ABC theory, 300–306, 314–318
renormalized, 322
fermion, in QED, 329–331
one-particle irreducible, 306
photon, in QED, 331–336
imaginary part of, 344–345
renormalized, 333–345
σ (Pauli) matrices, 68, 72, 85, 362
Slash notation, 110, 195
S-matrix, 156–158
Lorentz invariance of, 190
unitarity of, 156
ˆ
S-operator, 157–158
Dyson expansion of, 158
Lorentz invariance of, 166
Special relativity, 371–375
Spin matrices, 362
Spin-statistics connection, 191–195
Spin sums and projection operators, 408–
409
Spinor 68
conjugate, 110
four-component, 70
negative-energy, 75–76, 110
positive-energy, 74–75, 110
rest-frame, 72
and rotations, 89–92
self-conjugate (Majorana), 101–102,
212–213
two-component, 69, 72
and velocity transformations (boosts),
92–94
Spontaneously broken symmetry, 12, 15,
32
Standard Model, 3–4, 7, 41, 48, 61, 115,
146, 179, 299, 304, 343, 350–
352
Stokes’ theorem, 387
Strangeness, 9–10
conservation, 10, 35
Strange quark, 9–10
String theory, 4
Strong interactions, 26–29
Structure function, 271–272, 275–277
and positivity properties, 278
of proton, electromagnetic, 271–272
scaling of, 272–280
Subtraction, 323, 356
Sum rules, see Quark, parton model
Summation convention, 372
Super-renormalizable theory, 162, 318, 326,
353
Supersymmetry, 141
Symmetry
current, 186–187, 194, 207
internal, 57–58
operator, 184, 186–188, 194
Tau lepton, 5
and neutrino, 6