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1、 39 5 Vol39 No5 2020 5 COLLEGE PHYSICS May 2020 2019 08 30 2019 12 12 “ 351 ” 1965 櫍櫍櫍櫍櫍 櫍 櫍櫍櫍櫍櫍 櫍 殻 殻 殻 殻 “ ” 430072 O 412 A 1000-0712 2020 05-0010-04 【 DOI】 1016854/jcnki1000-0712190395 1-8 “ ” “ ” 3-6 Klein Gordon “ ” 7 Klein Gordon 7 Proca Proca 3 1 m 3 m x = x y z ict = x 1 x 2 x 3 x 4 m 4 m “

2、” q P N “ ” “ ” S A = A 1 A 2 A 3 A 4 S A =M A =1 2 3 4 1 M M = M = v 0 0 i v v 0 1 0 0 0 0 1 0 i v v 0 0 v 2 A 1 = v A 1 +i v A 4 3 5 “ ” 11 A 2 =A 2 4 A 3 =A 3 5 A 4 = v i v A 1 +A 4 6 v =1 / 1 v 2 /c 槡 2 v =v/c S、 S v S S x 1 、 2 3 6 A B =M m M n A m B n = mn A m B n =A n B n 7 1 4 A 2 1 +A 2 2 +

3、A 2 3 +A 2 4 =A 2 1 +A 2 2 +A 2 3 +A 2 4 8 x ict S S x x =x x x 2 + y 2 +z 2 c 2 t 2 =x 2 +y 2 +z 2 c 2 t 2 、 、 u u u =u u = 2 v v 2 c 2 = c 2 2 “ ” 2 “ ” 21 “ ” S J u = j x j y j z ic S J = j x j y j z ic j x j y j z 、 j x j y j z S S 、 S S J J =J J 9 j 2 c 2 2 =j 2 c 2 2 10 j 2 =j 2 x +j 2 y +j 2

4、z j 2 =j 2 x +j 2 y +j 2 z 10 j = v S S 0 S 0 j = v = 0 v 0 =0 = 0 j 2 c 2 2 =0 2 c 2 2 0 0 11 11 c 2 = 0 c 2 +j 2 12 2 = 2 0 + j/c 2 13 1、 2 1 2 22 “ ” S p u = p x p y p z iW/c S p = p x p y p z iW/c W、 W S 、 S p x p y p z 、 p x p y p z S 、 S p p =p p p 2 W 2 /c 2 =p 2 W 2 /c 2 14 W 0 =0 W 0 0 W 0

5、0 S v =0 m =m 0 W =W 0 =m 0 c 2 0 p =0 14 p 2 W 2 /c 2 =0 2 W 2 0 /c 2 0 15 15 W 2 =W 2 0 + pc 2 16 12 39 “ ” 9 23 “ ” S 5 A = A 1 A 2 A 3 A 4 = A i /c = A x A y A z i /c S A = A 1 A 2 A 3 A 4 = A i /c = A x A y A z i /c A x A y A z A x A y A z 、 S S A、 A 、 S S A A =A A A 2 2 /c 2 =A 2 2 /c 2 17 A 2

6、 =A 2 x +A 2 y +A 2 z A 2 =A 2 x +A 2 y +A 2 z S S 0 j = 0 v 0 =0 = 0 A =0 = 0 17 A 2 2 /c 2 =0 2 2 0 /c 2 0 18 2 = 2 0 + Ac 2 19 S r 0 x 0 y 0 z 0 q 0 0 x y z = q 0 r r 0 A 0 =0 = 0 x y z = 1 /4 0 V 0 x y z /r dV = q 0 /4 0 r = x x 2 + y y 2 + z z 槡 2 = x x 0 2 + y y 0 2 + z z 0 槡 2 S A 19 5 、 24 F

7、 “ ” S A 4 5 F A x A x = F =1 2 3 4 20 F = 0 B 3 B 2 i c E 1 B 3 0 B 1 i c E 2 B 2 B 1 0 i c E 3 i c E 1 i c E 2 i c E 3 0 21 S F A x A x = F =1 2 3 4 F F S S F =M m M n F mn 22 M v 2 E B E x =E x E y = v E y vB z E z = v E z +vB y 23 B x =B x B y = v B y + v c 2 E z B z = v B z v c 2 E y 24 F F = F

8、 F F F =2 B 2 E 2 /c 2 =F F =2 B 2 E 2 /c 2 25 S S B 2 E 2 /c 2 =B 2 E 2 /c 2 26 5 S S 0 v =0 S 0 B =B 0 =0 E = E 0 26 B 2 E 2 /c 2 =0 2 E 2 0 /c 2 E 2 =E 2 0 + Bc 2 27 4 5 10 11 q v S 5 “ ” 13 S S X v t =t =0 S r x y z 5 E =E 0 =q r / 4 0 r 3 B =B 0 =0 28 E 、 B S E / =E / E = v E v B 29 B / =B / B

9、= v B +v E /c 2 30 t =t =0 r = x y z S E x = qx 4 0 r 3 E y = v qy 4 0 r 3 E z = v qz 4 0 r 3 31 B x =0 B y = v E z /c B z = v E y /c 32 B =v E /c 2 33 t =t =0 x = v x y =y z =z E 、 E 0 B 27 t t 0 3 、 / 4 4 3 “ ” 2 1 2 2 2 3 “ ” “ ” 1 M 1991 97-115 122-123 182-191 2 M 2004 44-47 69 330-332 3 M 1994

10、153-154 181-183 4 M 2016 252-257 5 M 2008 96-97 168-170 180 176-177 126 6 J 2019 38 2 25-27 7 1 M 3 2000 581-584 587-590 8 J 2011 30 3 5-10 9 M 2 2012 10 M 2017 245246 11 M 2003 184-187 Several “ Pythagorean theorems ” in special relativity ZHOU Guo-quan School of Physics and Technology Wuhan Univer

11、sity Wuhan Hubei 430072 China Abstract Some teaching experiences about electrodynamics and special relativity are summarized Several rel- ativistic invariants and “ Pythagorean theorems ”in special relativity are derived by means of the tensor theory in four dimensional Minkowski space and the contraction operation rules of these tensors Meanwhile some application examples are given in illustration of these formulae Key words special relativity tensor relativistic invariant Pythagorean theorem four dimensional Minkowski space Lorentz transformation