| Date post: | 03-Jun-2018 |
| Category: |
Documents |
| Upload: | gypsy-singer |
| View: | 222 times |
| Download: | 0 times |
of 65
8/12/2019 Relativity Hilbert
1/65
arXiv:physics/9811
050v1
[physics.hist-ph]26Nov1998
http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v1http://arxiv.org/abs/physics/9811050v18/12/2019 Relativity Hilbert
2/65
8/12/2019 Relativity Hilbert
3/65
8/12/2019 Relativity Hilbert
4/65
8/12/2019 Relativity Hilbert
5/65
8/12/2019 Relativity Hilbert
6/65
8/12/2019 Relativity Hilbert
7/65
1/r2 r
8/12/2019 Relativity Hilbert
8/65
8/12/2019 Relativity Hilbert
9/65
8/12/2019 Relativity Hilbert
10/65
8/12/2019 Relativity Hilbert
11/65
8/12/2019 Relativity Hilbert
12/65
8/12/2019 Relativity Hilbert
13/65
8/12/2019 Relativity Hilbert
14/65
8/12/2019 Relativity Hilbert
15/65
8/12/2019 Relativity Hilbert
16/65
8/12/2019 Relativity Hilbert
17/65
8/12/2019 Relativity Hilbert
18/65
8/12/2019 Relativity Hilbert
19/65
8/12/2019 Relativity Hilbert
20/65
8/12/2019 Relativity Hilbert
21/65
8/12/2019 Relativity Hilbert
22/65
H
gd,
g d=dw1dw2dw3dw4 wi
H
H wi
8/12/2019 Relativity Hilbert
23/65
H
gH
g =
k
wk
gH
gkk,l
2
wkwl
gH
gkl,
, = 1, . . .4 gk g/wk gkl 2g/wkwl 1/2 1/4 kl H
K L
H
H=K+ L
K=K(g, gk , gkl) L= L(g
, qs, qsl) qsl =qs/wl
K
L
K+ L
8/12/2019 Relativity Hilbert
24/65
K
K=
gK,
K=
w
w
+
k,
(1/2)gK
8/12/2019 Relativity Hilbert
25/65
14
144 = 10
8/12/2019 Relativity Hilbert
26/65
H h
J(h) =,
H
gh +
,,k
H
gkhk +
,,k,l
H
gklhkl,
k l h wk wl J
(h)
h
gJ(h)
gJ(h) =
Hg
gh +
[gH]
h +D(h),
gH
= 0 D(h)
H
gH
h
p =s
(gs ps gsps gsps ) ,
pjs=
pj
ws
p
Lpg = p(;)
ps p
8/12/2019 Relativity Hilbert
27/65
p g
x
x
+p
(x)
p h ps psk
gJ(p) =
Hg
gp +E+D(p),
D(p) E
E=
Hg
ggs +
gH
ggs +
gH
gkgsk +
gH
gklgskl
ps
(gsps + gsps ) [gH]+gH
gkgs +
gH
gklgsl gs
wl
gH
gkl
psk.
es els E
E=s
esps +
s,l
elspsl .
es els es
ws
es=d(g)
gH
dws,
p
p
ps
ps
8/12/2019 Relativity Hilbert
28/65
(g)
E
gJ(h) p h
gJ(p) E
ws
E=D(h)
h=p
D(p),
E
wl psl
l
elswl
= 0
es
es= 0.
g qs
8/12/2019 Relativity Hilbert
29/65
J n n
n
n n4
J g
8/12/2019 Relativity Hilbert
30/65
qs s
Jws
ps =P J,
P =Pg+Pq,
Pg =,,l,k
p
g +pl
gl+plk
glk
,
Pq = l,kpl
ql
+plk
qlk ,
pl =s
(qlsps +qsp
sl ),
plk =pl/wk ws J g gl g
lk ql qlk ws
J p
[gJ]
p =
s,l
(isps +ilsp
sl ),
is = [gJ]
gs ,
ils =2
[gJ]sgl,
8/12/2019 Relativity Hilbert
31/65
is=l
ilswl
g
u = u(x1, x2, x3, x4) a u/x x
(aij ; ui)dx1dx2dx3dx4 = 0,
Xx
X= 0,
a=X,
u=X.
J K =
gK
gJ
gG =
g(K (1/2)gK)
Gls;l= 0
8/12/2019 Relativity Hilbert
32/65
u
eij i, j= 1, 2, 3 a
u
a a
x=
x(
Xa),
x
T=
aX,
Div T = 0.
aa aX uX
S=
(a a)X uX
8/12/2019 Relativity Hilbert
33/65
H qs qsl
qs qsk
H L
,,m
L
g(gmpm+g
mpm) s,m
L
qsqmp
ms
s,k,m
L
qsk(qsmp
mk +qmkp
ms +qmp
msk) = 0,
L pmsk L
Mks = qsk qks.
H=K+L
L H qs
8/12/2019 Relativity Hilbert
34/65
pm L Mks
2
gL
g gm =
g
Lm
L
qmq
s
L
MmsMs
.
L g
L
g
8/12/2019 Relativity Hilbert
35/65
8/12/2019 Relativity Hilbert
36/65
gL g
[gK]
+
gL
g = 0,
H=K+L ils
2
gL
g gm =im.
i =
im
/wm
i=m
wm
gLm +
gL
qmq+
s
gL
MsmMs
,
[gL]
m
=gL
qm s
ws
gL
qms
Msm i L/qsm =L/qms
m
Mm[
gL]
m+q
wm[gL]
m
= 0.
8/12/2019 Relativity Hilbert
37/65
q= 0 gL
m= 0 w4 =
gL4
/w4 = 0 gLi
/w4 i = 1 2 3
L
Mm
L =MM(gg gg)
8/12/2019 Relativity Hilbert
38/65
8/12/2019 Relativity Hilbert
39/65
8/12/2019 Relativity Hilbert
40/65
8/12/2019 Relativity Hilbert
41/65
8/12/2019 Relativity Hilbert
42/65
8/12/2019 Relativity Hilbert
43/65
8/12/2019 Relativity Hilbert
44/65
gJ(p) J(p)
H g
E=esps +elsp
sl
E= [gH]p +
D
(h)(h=p) D(p)
.
es gH
H
gH
P(gH) = Pg(
gH) + Pq(
gH)
ps P(
gH)
P(gH) =
[gH]
p +
k
[gH]
kpk+
g(al +bl +cl +dl)
wl
8/12/2019 Relativity Hilbert
45/65
al =,,k
H
gkl
pk +
k
p +
k
p
,
bl =,,,k
H
gl
wk
H
glk H
glk
k
H
glk
k
p,
cl =kl
H
qklpk,
dl = 1
2g
k,s
wk
gH
qlk
gH
qkl
psqs
ps
P(gH)
P(gH) =
s
gHps
ws.
el
=Hpl
al
bl
cl
dl
ps
l
gel
wl= 0
Lpl k
L
qklpk 1
2g
k,s
wk
gL
qlk
gL
qkl
psqs
,
8/12/2019 Relativity Hilbert
46/65
el al bl cl
dl
L L Mkl
s,k
Lls
L
MlkMskL
qlqs
ps.
H H = K+ L K L qs qsl g
[gK]
=
g(K12Kg),
K g
K g
8/12/2019 Relativity Hilbert
47/65
K gK
el H K
L L qs Msl L
g
1/2 gK
T
T 1g
gL
g
g=|g|= 1
g
8/12/2019 Relativity Hilbert
48/65
K
8/12/2019 Relativity Hilbert
49/65
8/12/2019 Relativity Hilbert
50/65
H g qs
g , = 1, 2, 3, 4
ws qs
ws
g , = 1, 2, 3, 4
ws
qs
8/12/2019 Relativity Hilbert
51/65
K 12gK
Kgdw
K 12gK Kgdw
8/12/2019 Relativity Hilbert
52/65
g
8/12/2019 Relativity Hilbert
53/65
8/12/2019 Relativity Hilbert
54/65
8/12/2019 Relativity Hilbert
55/65
8/12/2019 Relativity Hilbert
56/65
8/12/2019 Relativity Hilbert
57/65
8/12/2019 Relativity Hilbert
58/65
8/12/2019 Relativity Hilbert
59/65
8/12/2019 Relativity Hilbert
60/65
8/12/2019 Relativity Hilbert
61/65
8/12/2019 Relativity Hilbert
62/65
8/12/2019 Relativity Hilbert
63/65
8/12/2019 Relativity Hilbert
64/65
8/12/2019 Relativity Hilbert
65/65
![Research Article Some Definition of Hartley-Hilbert and ...downloads.hindawi.com/journals/jmath/2014/790161.pdf · andtostrongBoehmiansin[]. e Hartley-Hilbert and Fourier-Hilbert](https://static.documents.pub/doc/80x56/5edc9aa7ad6a402d666756a2/research-article-some-definition-of-hartley-hilbert-and-andtostrongboehmiansin.jpg)
