Mathematical Principles of Theoretical Physics
6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 387 are the sectors ofSU(N 1 )andSU(N 2 )gauge fields for the electromagnetic intera ...
388 CHAPTER 6. QUANTUM PHYSICS By (6.5.39)-(6.5.41), the equations (6.5.42)-(6.5.43) are written as Rμ ν− 1 2 gμ νR=− 8 πG c^4 T ...
6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 389 molecules atoms nucleons electrons naked quarks gluon clouds weaktons gluons w∗- ...
390 CHAPTER 6. QUANTUM PHYSICS 1.Classical theory of atomic shell structure. We recall that an atom with atomic number Zhas ener ...
6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 391 Thus, we have two kinds of classifications (6.5.55) and (6.5.56) of sub-systems ...
392 CHAPTER 6. QUANTUM PHYSICS B. FIELD EQUATION OF SYSTEMSnl. The precise model of atomic spectrum should take (6.5.56) as anN- ...
6.5. FIELD THEORY OF MULTI-PARTICLE SYSTEMS 393 The equations (6.5.66)-(6.5.68) need to be complemented with some gauge fixing e ...
394 CHAPTER 6. QUANTUM PHYSICS ...
Chapter 7 Astrophysics and Cosmology The aim of this chapter is to study fundamental issues of astrophysics and cosmology based ...
7 Astrophysics and Cosmology Based on the black hole theorem, theorems on the structure and origin of the Universe are proved in ...
7.1 Astrophysical Fluid Dynamics the pressure term is (7.1.7) ∇p= ( g^1 k ∂p ∂xk ,···,gnk ∂p ∂xk ) , the divergence ofuis (7.1.8 ...
398 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY where(r,θ,φ)is the spherical coordinate system, andu=u(r,t)andv=v(r,t)are functions of ...
7.1.5 Astrophysical Fluid Dynamics Equations Thus, by (7.1.4) and (7.1.19) we getRμ νas (7.1.20) R 00 =eu−v [ − 1 2 u′′− 1 r u′+ ...
400 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY Comparing (7.1.25) with (7.1.15), we can obtain b= 2 mG c^2 . Thus, we get the solutio ...
7.1. ASTROPHYSICAL FLUID DYNAMICS 401 By (7.1.20) we have R=gμ νRμ ν=−e−uR 00 +e−νR 11 + 2 r^2 R 22. Then, by (7.1.20) andRνμ=gν ...
402 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY We are now in position to discuss the solutions of problem (7.1.28)-(7.1.33). Let (7.1 ...
7.1. ASTROPHYSICAL FLUID DYNAMICS 403 In this case, we have M(r) = 4 π 3 ρ 0 r^3 for 0≤r≤R, ρ 0 = 3 4 π m R^3 . Thus we obtain t ...
404 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY In (7.1.43) we have g 11 =α(r), g 22 =r^2 , g 33 =r^2 sin^2 θ, gij=0 fori 6 =j. By (7. ...
7.1. ASTROPHYSICAL FLUID DYNAMICS 405 2) By (7.1.6) and (7.1.45),(u·∇)ukcan be written as ukDkuθ=ur ∂uθ ∂r +uθ ∂uθ ∂ θ +uφ ∂uθ ∂ ...
406 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY ̃∆is the Laplace operator for scalar fields given by (7.1.58) ̃∆T= 1 r^2 sinθ ∂ ∂ θ (s ...
«
16
17
18
19
20
21
22
23
24
25
»
Free download pdf