臺灣博碩士論文加值系統

　　在光前座標場論中，手徵對稱的定義與一般慣用的等時間場理論是有很大的差異。我們從探討在自由費米子理論手徵變換的自恰性開始。然後延伸到探討在光前量子色動力學的手徵對稱性。同時，我們得到在光前場論中一完整的、新的光前軸－向量流。物理上，在光前量子色動力學的手徵對稱性的破壞只與夸克膠子間的螺旋性翻轉作用有關。值得注意的，這新的軸－向量流包含了一些物理含義。我們分為兩方面來探討，在光前場論的自發對稱破缺機制及強子變遷矩陣元中新的光前軸－向量流不包含π介子極部分因此對應的手徵電荷可平滑地描述各種與π介子變遷有關的強子過程的現象。

　The definition of chiral transformations in
light-front field theory is very different from the conventional form in equal-time formalism. We begin from studying the consistency of chiral
transformations in free fermion theory. And then we extend to studying the chiral symmetry in light-front QCD. Meanwhile, we derive a complete new light-front axial-vector current for light-front field theory. Physically, the breaking of chiral symmetry in light-front QCD is only associated with helicity flip interaction between quarks and gluons. Remarkably, the new
axial-vector current does contain some physical implications. We study in two aspects, the spontaneous chiral symmetry breaking in light-front formulation and the feature of hadronic transition matrix element in which the new light-front axial-vector current does not contain the pion pole part so that the associated chiral
charge smoothly describes pion transitions for various hadronic processes.

Table of Contents v
Abstract vii
Acknowledgements viii
1 Introduction 1
2 Light-front QCD 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Canonical Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 The perturbation structure in LFQCD . . . . . . . . . . . . . . . . . 14
2.3.1 The x+-ordered perturbation theory . . . . . . . . . . . . . . . 14
2.3.2 Momentum space representation . . . . . . . . . . . . . . . . . 16
2.3.3 Diagrammatic rule . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Chiral transformation in the light-front QCD 20
3.1 Light-front chiral transformation in Free fermion theory . . . . . . . . 20
3.1.1 The contraction . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.2 The definition of light-front chiral transformation . . . . . . . 23
3.2 QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Chiral anomalies 30
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 The basic ideal of the point-splitting technique . . . . . . . . . . . . . 31
4.3 Chiral anomalies associated with light-front axial-vector current . . . 35
4.3.1 The residual gauge invariance . . . . . . . . . . . . . . . . . . 35
4.3.2 Derivation chiral anomaly of light-front axial-vector current . 36
5 Physical implication of light-front axial-vector current 42
5.1 Spontaneous symmetry breaking . . . . . . . . . . . . . . . . . . . . . 42
5.2 Hadronic transition process . . . . . . . . . . . . . . . . . . . . . . . 45
6 Conclusion 48
A Adiabatic ”switching on” 50
B Local Chiral transformation 51
B.1 Free fermion theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
B.2 light-front QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
C Calculation of commutation relation [ ˜Q5, ‾ ψγ5ψ] 55
D Calculation of the last two terms in eq. (4.24) 57
Bibliography 59

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