Dirac particles in uniform magnetic fieldDescripción completa
Dirac particles in uniform magnetic fieldFull description
This is a presentation i often use to introduce particle colliders to university students.
Descripción: SG _SST, formatos, guias.
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Dirac particles in uniform magnetic field
Descripción completa
12Full description
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Meningkatkan Disiplin Kerja Untuk Memperkecil Resiko Kecelakaan Kerja Di MV. JENNIFERFull description
Particle physics units: This problem builds familiarity with the convention, 26 +34 −8 1 m 1 1 ℏ = c = 1 ↔ J ⋅ s = 6.626 × 10 ; s = 3 × 10 ; J ⋅ m = 6.626×3 × 10 ;
(1.1)
in which all physical quantities are expressed in units of energy to the appropriate power. In high-energy particle physics physics a typical typical unit of of energy is, is, 10
GeV
9
= 10
−10
= 1.602 × 10
eV
J
=
1.602 32
−10 + 2⋅( −8 )
× 10
1.602 9
kg =
−26
× 10
kg
=
1.602 ×10− J
10
=
1.602 × 10− 6.626 2π
ℏ
×10
−34
1
(1.2)
s
(a) What is Newton's constant G N N in units of the appropriate power of GeV ? Doing the calculation with rough approximations indicated in (1.1), G N
=
G0 =
GN
= N
6.67 ×10−11 −2
cSI
m2 kg 2
1 ℏ SI cSI
cSI
2
eSI
2
=
eSI 2
=
cSI
5
ℏ SI
kg
m m2 s 2 kg 2
=
(
1 × 3
10
−8
)
1.00 × 10 −28 GeV −2
≈
m
2
(
=
kg
↔
1 × 3
10
1 2 ( 6. 6.626 / 2π )×3 −8
)
×10
(
26
=
1 3
× 10
−8
)
2
eV 19 1.602×10−
J ⋅ kg
2π × 6.626×3
⋅
eV
1026
−1 9 1.602 ×10 ( 3×10 108 ) 2
(1.3)
GN = 6.68 × 10−39 GeV −2
Doing the same calculation with Mathematica and plugging in as many significant figures as possible, we re39 present the results (1.3) with higher accuracy, we get G N = 6.70837 ×10 − .
What mass in GeV would an electron need to have in order for the gravitational attraction between two electrons to be of the same order as the Coulomb repulsion between them? F
=1=
FG
?2
=
GN me
FC
ke
↔
2
? e
m
=
ke 2
2
=
N ⋅ mC 2 ⋅ [1.602 ×1 0 −19 ]2 C 2
1.59 ×10
GN
−29
−2
GeV
1026 2π ⋅6.626×3
=
⋅ [1.602 ×10
1.59 ×10
−29
−19
]2
−2
GeV
=
3.59 × 10 7 GeV (1.4)
What is the actual electron mass? me
= 9.11 × 10 10
−31
kg
= 9.11 × 10 10
− 31
9 1.602
× 10
26
GeV
=
5.12 ×10 1 0−4 GeV
− 11
= 1.42 ×10 10
?
me
?
<< me
(1.5)
The large discrepancy between these two masses is a manifestation of the gauge hierarchy problem . (b) The energy scale of G N N derived in (a) also defines unique mass, time, and length scales, known as the Planck mass, Planck time, and Planck length. What are these in everyday units (say, grams, seconds, and meters)?
The respective scales are appropriate powers of the gravitational constant, G N, which is from (1.3), m p
=
1 G N
1
=
6.71×10
GeV −39
19
= 1.22 × 10
GeV ×
1.602 9
×10
−26
kg
GeV
=
8
2.17 ×10 − kg
(1.6)
Something that is nice is that the Planck length and time are the same (since c = 1 ), c = 1 ↔ t p
= ℓp =
1.602 ×10−10 GeV −1 −20 −1 G N = 8.17 × 10 GeV × 6.626 −34 s 2 ×10
−1
=
44
5.38 × 10 − s ;
ℓ p = ct p =
35
1.61×10 − m (1.7)
π
Wikipedia says, τ p
=
ℏG
c
5
= 5.39 × 10
−44
s; mp
=
ℏc
G
=
8
2.18 ×10 − kg;
ℓp =
ℏG
c
3
=
cτ p
= 1.62 × 10
−35
m;
(1.8)
I’m not sure how to “derive” these. m p
=
1 G N
; tp
=
G; c =1↔ ℓ p
=
G
= tp =
Simple dimensional analysis implies that all quantities in our universe should be of order these fundamental scales. The large discrepancy between the Planck time and the age of the Universe manifestation of the cosmological constant problem.)
