Advanced Field Theory Book

	Preface
1	Micro and Macro Physics	1
1.1	Micro, Macro, and Thermal	1
1.2	Classical Physics for Particles and Fields	3
1.3	Quantum Mechanics and Quantum Field Theory	8
1.4	The c-q Transmutation Condition	12
1.5	Matter and the Vacuum	13
2	Vacuum Correlation	15
2.1	Number Representation	15
2.2	Coherent, Squeezed or Thermal-Like States	16
2.2.1	Coherent States	16
2.2.2	Squeezed States	19
2.2.3	Two-Mode Squeezed States	21
2.2.4	An Equivalence Theorem	23
2.3	Noise in Pure States	24
2.3.1	Thermal-Like Noise in the Two-Mode State	24
2.3.2	Correlation through the Vacuum	26
2.4	Pure State and Mixed State	28
2.4.1	Bosonic System	28
2.4.2	Thermal Vacuum for Fermionic Oscillators	30
2.4.3	Non-Trivial Parameters in Vacua	32
2.5	TFD Mechanism for Noise Creation	33
2.6	TFD Mechanism and Black Hole	34
2.7	Phase and Time Operators in TFD	35
3	Inequivalent Vacua	39
3.1.1	Infrared Catastrophe of Bremsstrahlung	39
3.1.2	Vacuum Polarization	40
3.1.3	Renormalization	42
3.2	Many Vacua	42
3.3	Anomalous Operators	45
3.4	Pure State and Mixed State	46
3.4.1	Bosonic Systems	46
3.4.2	Fermionic Systems	47
4	Quasi-Particle Picture	50
4.1	Modern Particle Picture and the Old Atomism	50
4.2	Countably Infinite Degrees of Freedom	50
4.3	Continuous Set of Number States	52
4.4	Quasi-Particles and Dynamical Map	52
4.5	Time-Independent Global Operators	55
4.6	The Dynamical Map of the Hamiltonian	57
4.6.1	Quasi-Particle Free Hamiltonian	57
4.6.2	Reactions among Quasi-Particles	59
4.6.3	Asymptotic Fields and Quasi-Particles	59
4.6.4	Many Choices for Incoming Particles	61
4.6.5	Renormalization	62
5	Ordered States	64
5.1	Spontaneously Broken Symmetries	64
5.1.1	A Physical Picture	64
5.1.2	A Mathematical Picture	65
5.1.3	Symmetry Rearrangement	67
5.1.4	Boson Transformation	68
5.1.5	Low Energy Theorem I	69
5.1.6	Generators and the Nother Current	69
5.1.7	The Ward-Takahashi Relations	70
5.1.8	[Theta]-Selection	71
5.1.9	Summary of this Section	73
5.2	Broken Phase Symmetry in a Scalar Model	74
5.2.2	Model	74
5.2.3	The Nother Current and the Generator	74
5.2.4	Phase Symmetry Rearrangement	75
5.2.5	The Order Parameter and [Theta]-Selection	75
5.2.6	The Dynamical Map of the Current	76
5.2.7	A Fluctuation Effect	76
5.2.8	A Strategy for Computational Analysis	78
5.2.9	Superfluid Current	79
5.3	Superconductivity	79
5.3.2	The BCS Model	80
5.3.3	The Current and the Generator	81
5.3.4	Phase Symmetry Rearrangement	81
5.3.5	The Dynamical Map of Charge Density	82
5.3.6	The Nambu-Goldestone Field	82
5.3.7	Are NG-Bosons Entirely Eliminated?	83
5.3.8	Order Parameter and [Theta]-Selection	84
5.3.9	A Fluctuation Effect	85
5.3.10	Gauge Invariance	86
5.3.11	A Strategy in Computational Analysis	87
5.4	Non-Abelian Symmetry Breakdown	88
5.4.1	Spontaneously Broken Spin Symmetry	88
5.4.2	Symmetry Rearrangement	91
5.4.3	Low Energy Theorem II	92
5.5	c-q Transmutation and Crystal Phonon	93
5.6	The Spontaneous Creation of Mass	95
6	Macroscopic Objects	99
6.1	Boson Transformation	99
6.1.2	Planck's Constant	99
6.1.3	Boson Transformation	100
6.1.4	Induced Potential and Zero-Energy Mode	102
6.1.5	Quantum Mechanical Operators	105
6.1.6