

2004: 粒子與場 
Local Program 1: Physics and Mathematics of Gauge Field Theories：
Program Coordinator: Chopin Soo (NCKU)
Participants:
Chen ChuanHung (NCKU),
Chen ChiaChu (NCKU),
Huang WungHung (NCKU),
Li HsiangNan (NCKU + AS),
Nyeo SuLong (NCKU),
Soo Chopin (NCKU),
Yo HweiJang (NCKU) ,
Zhang WeiMin (NCKU),
Lee ChinRong (NCCU),
Su WangChang (NCCU),
Tu MingHsien (NCCU),
Chen YawHwang (Kun Shan U. of Tech., Tainan),
Wu ChunYi (Fortune Inst. of Tech., Kaoshiung),
Hwang ChienWen (NKNU, Kaoshiung),
Lin DeHone (NSYSU),
Postdocs, Shortterm visitors (visitor list is still under consultations), and graduate students
Focus: Methods and phenomenology of quantum gauge field theories
Regularization techniques, Lightfront formalism, Operator Product Expansions, path integral techniques, and their applications to chiral field theories and quarkhadron phenomenology; and applications of differential geometry and topology to gauge field theories
Details:
Quantum field theory (QFT) is the standard framework for describing elementary particles and their interactions. Central to its success has been the incorporation and study of gauge field theories which lie at the heart of the standard model and its extensions. We propose to explore new applications and phenomenology, and to concentrate on the above topics on which we also have past experience and common interests so as to enhance interactions, mutual learning, and collaborations among the paricipants.
In the study of gauge field theories, differential geometry and topology have become essential tools for theoretical physicists. Their use have lead to many results and insights which cannot be obtained otherwise. They have greatly helped to unravel and reveal the subtleties and richness inherent in gauge field theories. We aim to increase crossfertilizations between more mathematically oriented participants working on soliton physics, integrable systems and differential geometric methods in curved spacetimes with phenomenologists. In particular, the identification of physical degrees of freedom in effective theories and new applications and implications of monopole, instanton solutions and skyrme models will be investigated.
Computations in a quantum field theories involve quantum loop calculations that are generally plagued by infinities, and thus regularization is called for. A commonlyused method is dimensional regularization, which respects gauge and Lorentz symmetries. However, it is not well suited to chiral theories like the standard model of particle physics and lowenergy hadron physics with axial vector currents. We propose to investigate how differential regularization (DR) and other invariant regularization schemes can be fully implemented in a consistent manner in chiral theories. The investigations will include backgroundfield formalism for DR. For the gauge sector, which requires gauge conditions, we shall consider using the VilkovskyDeWitt approach to assure gaugeindependence of physical quantities. DR was introduced several years ago and demonstrated to be applicable to chiral gauge theories. It does, however, exhibit some inconveniences e.g. fixing the renormalization scale in gauge theories requires implementing the Ward identities by hand. We shall thus first apply DR to gauge theory in the backgroundfield formalism, which is a useful computational tool in quantum field theories that allows one to compute radiative corrections while maintaining manifestly the symmetries of the theory under consideration. In essence, this formalism allows us to manipulate a gauge theory as a scalarlike theory. Therefore, by studying gauge theories in this formalism with DR, we hope to eliminate the cumbersome step of implementing the Ward identities in the calculations of Green functions, and hope that this method can be applied more easily to computations.
Another regularization scheme uses zeta functions[1]. Recently we proposed a regularization of von Neumann entanglement entropy in terms of generalized zeta functions[2]. This Lorentz invariant characterization allows the discussion of entanglement issues in quantum information science in the context of quantum field theory and systems with infinite dimensional Hilbert spaces. Its serious study and application to the thermodynamics of entanglement may yield significant results in quantum information science.
On the other hand, a longstanding problem in the last thirty year investigations of theoretical science is how to solve nonperturbatively the physics of quantum chromodynamics (QCD). QCD, the theory of the strong interaction, is a theory in physics that has been accepted widely as fundamental but has not been precisely tested. The lack of precision tests come from the fact that we are still unable to apply QCD to describe strong interaction processes at low and intermediate energies, although many of these processes have been measured for a long time. Loosely speaking, all successful methodologies developed in 20th century lie more or less on various perturbative methods. Nonperturbative approaches in field theories were mainly proposed by K. G. Wilson in 70's to 80's of the last century, such as the renormalization group approach and the lattice gauge theory. Some progresses have been make in solving QCD in the past based on these methods, but it is still far to reach upon a satisfied answer. Less than 10 years ago, the investigations of the nonperturbative QCD turns to the lightfront formalism. The lightfront formulation is the nature framework for relativistic physics, so does for nonperturbative field theory.
With almost 10 years research experience on lightfront in the past, we can now focus on the most difficult problem of how to provide a clear picture of the dynamical chiral symmetry breaking and the quark confinement with a trivial lightfront QCD vacuum. The trivial vacuum in lightfront is obtained by removing the longitudinal zero modes which can be easily realized by imposing an explicit cutoff on small longitudinal momentum or via a suitable prescription of the longitudinal zeromode[3]. Both methods give a specific regularization of the longitudinal momentum going to be zero. It is then natural to ask how the spontaneously chiral symmetry breaking and quark confinement (which are a nontrivial vacuum effect of QCD in common understanding and plays a crucial role in the description of low energy hadronic physics) can be manifested in lightfront. A few years ago, the quark confinement has received certain understanding on the lightfront[4]. Meanwhile, Wilson pointed out that the concept of spontaneously chiral symmetry breaking may be realized via an explicit symmetry breaking in lightfront induced from counterterms of removing the longitudinal momentum divergence[5], but up to date a practical scheme of this procedure has been carried out yet.
In fact, chiral symmetry itself is not a good dynamical symmetry for the strong interaction. Mechanisms of a dynamical symmetry breaking can manifest differently in different spacetime framework. Therefore, before we attempt to describe the chiral symmetry related counterterms through a reliable renormalization procedure for the lightfront QCD Hamiltonian, it is certainly helpful to understand the precise meaning of chiral symmetry and its breaking in lightfront. Currently, we are studying, from the very first principles, chiral transformations in lightfront and the corresponding theorems of axialvector current for the lightfront QCD. We are sure that the further exploration of its relation with the poinic dynamics and the associated physical implication in hadronic structure will be greatly helpful for our understanding of nonperturbative QCD in lightfront.
Also, based upon past experience, our participants shall also investigate applications of operator product expansions, lightfront formalism, and apply the regularization schemes to effective Lagrangians for the lowenergy hadron physics which incorporate relevant features of QCD.
In particular, we shall take advantage of the formalism of the lightfront dynamics in the framework of the quark model, which can treat relativistic effects of quark motion and spin in bound states, and phenomenological wave functions to study (1) the parton distribution functions in the deep virtual Compton scattering (DVCS) and (2) the transition form factors between swave and pwave mesons. Our motivations can be described as follows:
On the empirical side, data on electronproton scattering (HERA in Germany, SLAC in USA) and electronmeson scattering (Fermilab in USA) are available; but in the analysis of lightfront quark model (LFQM), there is nonvalence contribution in which the treatment is still uncertain. The difficulty comes from the fact that one does not fully know how to use the concept of parton to explain the final hadron in the nonvalence configuration. Ref. [6] contains details of the source of nonvalence contributions and the difficulties involved and a consistent treatment for the valence and nonvalence configurations in the semileptonic weak decays. Subsequently, this approach is applied to the electronhadrons DVCS and to obtain the socalled ``skewed parton distribution functions” which are a generalization of the ordinary parton distribution functions and elastic form factors and subsequent calculation of all the form factors in the electronmeson elastic scattering. Indeed, the form factors of the electronhadron elastic scattering connects compactly to the parton distribution functions of the electronhadrons inelastic scattering. And from the LFQM, we find the latter process has the above nonvalence contribution. Thus we can treat the results of the electronmeson scattering as constraints, and use the approach in Ref. [6] to calculate the parton distribution functions of electronparton DVCS. Comparing with the data which has been or will be obtained from the above experiments, we can further constrain the internal structure of the hadronic bound state.
Increasing amount of data from B factories (KEK in Japan, SLAC in USA) has also induced the study of the decay modes including pwave mesons, and especially in B > D(*, 1/2, 3/2) . Based on the experience of studying transitions between swave and swave mesons, we shall apply the lightfront approach to calculate the form factors between swave and pwave mesons. The pwave mesons include scalar, axial vector, and tensor mesons; as to the decay modes, there are semileptonic and radiative decays. In addition, we may also consider these transitions in the heavy quark limit. It is well known [7] the various form factors will reduce to two functions, and we may also use the phenomenological wave function to compare the results with the IsgurWise function.
Another subtopic of interest is the study of Lorentz and discrete symmetry violations. It is well known that homogeneous Lorentz transformations consist of boosts and rotations. Lorentz symmetry not only guarantees the speed of light being the same in every inertial frame but also implies angular momentum conservation. Precision empirical measurements have so far produced no evidence of any deviations from Lorentz invariance. In addition, we also know that quantum field theory, the modern description of all interactions among particles, at least at energies well below the Planck scale, is founded upon the synthesis of quantum mechanics and Lorentz invariance. In the framework of QFT, it was proved that if the conditions of locality, unitarity and Lorentz invariance are satisfied, CPT has to be conserved. This is the socalled CPT theorem [8]. Nevertheless, possible mechanisms for the breaking Lorentz symmetries and/or CPT transformations have been found in theories which may describe physics at the Planck scale. Firstly, according to the study of Refs. [9], curved space times around black holes in quantum gravity will violate unitarity because a portion of information will disappear inside the microscopic event horizons. Chiral gravity which is fully compatible with Lorentz invariance may also violate CPT because of its nonHermitian couplings to torsion fields[10]. Furthermore, due to the nonlocal nature of strings, it was shown that in string theory [11] spontaneous Lorentz symmetry breaking can arise from tensor fields with nonvanishing low energy vacuum expectation values. Possible modifications to Lorentz invariant high energy particle dispersion relations may also come from noncommutative spacetimes, models of spacetime foam, and loopquantum gravity scenarios. These have lead to recent proposals of doublyspecial relativity theories that involve both an observerindependent velocity scale and an observerindependent length/momentum scale[12].
As no Lorentz and CPT violations have so far been observed in nature, such effects if they exist are presumably tiny. Therefore, the accuracies of experiments should be push to unprecedented levels. However, in recent years a number of sensitive experiments, such as atomic systems[13], photons[14], hadrons[15] as well as muons[16] and electrons[17], have participated to detect the violations of Lorentz and CPT symmetries. One particularly sensitive class of experiments involves extremely precise clocks and resonators. A number of experiments of this type are under development to test relativity principles on the International Space Station (ISS). These include the atomicclock based experiments ACES [18], PARCS, RACE [19] and a resonantcavity experiment, SUMO [20]. Some of the best constraints on Lorentz and CPT violation have been achieved in Earthbased atomicclock experiments. Recently, similar techniques have been used in Earthbased experiments involving superconducting microwave cavities and cryogenically cooled optical cavities that probed previously untested regions of coefficient space. The basic principle behind all these experiments is to search for variations in the frequencies of resonant systems as the Earth rotates, while spacebased versions will look for the variations in satellites orbiting the Earth. We plan to study (1) the implication of CPT violation on electric dipole moment of lepton (2) the oscillation of neutronantineutron in quantum gravity decoherence. Their motivations are briefly described as follows:
(1) It is known that the operator for electric dipole moment is Podd and Todd. If the interaction term is also Ceven, a nonvanishing electric dipole moment can be obtained. Due to the C conservation, the corresponding electric dipole moment for the antiparticle should be of opposite sign to that of the particle. Hence, their sum should vanish. However, if there is a Codd interaction involved, the electric dipole moment for particle and antiparticle bear the same sign, and their sum does not vanish anymore. Thus different electric dipole moments for particle and antiparticle can manifest the effects of CPT violation. The current limit on electric dipole moment of electron has reached 1027 ecm, and it can reveal CPT violation of the same order of magnitude from the difference between electron and positron dipole moments. We shall find out what models of CPT violations can reach the current experimental limit.
(2) The induced decoherence and oscillation for KantiK mixing in quantum gravity have been introduced in Ref.[21]. It is of interest to also study the effects of quantum gravity on the phenomenon of the oscillation of neutronantineutron. Although the phenomenon is similar to neutral K meson system; the latter however involves baryon number violation; and it is worth mentioning if oscillating neutrinos are Majorana (with lepton number violation), our method of investigation may also apply to neutrino oscillations.
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Relevant (selected) publications/preprints of investigators

Spontaneous CP violation from highdimensional operators, D. Chang, C.H. Chen and C.Q. Geng , Prog . Theor . Phys. 101, 403 (1999)

T violation in B to K* l  l + from SUSY, C. H. Chen and C. Q. Geng , Phys. Rev. D66 (2002) 014007

CP Violation in Hyperon Decays from SUSY with Hermitian Yukawa and A Matrices, C. H. Chen , Phys. Lett . B521 (2001) 315319

T violation in L b to L l + l  decays with polarized Λ, C.H. Chen , C.Q. Geng and J. N. Ng, Phys. Rev. D65, 091502 (2002)

The Muon Anomalous Magnetic Moment from a Generic Charged Higgs with SUSY, C.H. Chen and C.Q. Geng , Phys. Lett . B511, 77 (2001).

Effective Potential of Nambu  JonaLasinio Model in Differential Regularization, Y.H. Chen and S.L. Nyeo , Chinese Journal of Physics 33, 213220 (1995)

Differential Renormalization of QCD in the BackgroundField Method, S.L. Nyeo , Chinese Journal of Physics 34, 874880 (1996))

Differential Renormalization of Scalar Field Theory in the BackgroundField Method, Y.H. Chen , M.T. He, and S.L. Nyeo , Chinese Journal of Physics 34, 11291135 (1996)

The U_ L( 3) X U_R(3) Extended NambuJonaLasinio Model in Differential Regularization, Y.H. Chen , S.L. Nyeo , and Y.W. Yang, Int. J. Mod. Phys. A12, 23612371 ( 1997)

Charge form factors and transition form factors of light mesons in LFQM, C. W. Hwang , Eur . Phys. J. C19 (2001) 105

Consistent treatment for pion form factors in spacelike and timelike regions, C. W. Hwang , Phys. Rev. D64 (2001) 034011

Lepton pairs decay of K L meson in the lightfront model, C.Q. Geng and C. W. Hwang , Phys. Rev. D66 (2002) 034005.

Mesonic tensor form factors with light front quark model, C.Q. Geng , C. W. Hwang , C.C. Lih and W.M. Zhang , Phys. Rev. D64 (2001) 114024

Consistent treatment for pion form factors in spacelike and timelike regions, C. W. Hwang , Phys. Rev. D64 (2001) 034011

C.Y. Cheung, C.W. Hwang , and W.M. Zhang , Z. Phys. C75 (1996) 657

Covariant lightfront model of heavy mesons within HQET, H.Y. Cheng, C.Y. Cheung, C. W. Hwang and W.M. Zhang , Phys. Rev. D57 (1998) 5598

B > p l n form factors calculated on the light front, C.Y. Cheung, C.W. Hwang and W.M. Zhang, Z. Phys. C75 (1997) 657

Mesonic form factors and the Isgur Wise function on the light front, H.Y. Cheng, C.Y. Cheung, and C.W. Hwang , Phys. Rev. D55 (1997) 1559

Temporal gauge field theory in the Feynman prescription, K. C. Lee and S .L. Nyeo , J.Math.Phys.35:22102217 ,1994

THE PLANAR GAUGE IN A NEW FORMALISM, G. Leibbrandt and S.L. Nyeo , Mod. Phys. Lett . A3 ,1085 1090 (1988)

Application of unifying prescription for axial type gauges in QCD, G. Leibbrandt and S.L. Nyeo , Phys. Rev. D39, 1752 (1989)

YangMills theory in the light cone gauge in the BecchiRouetStrora formalism, S.L. Nyeo , Phys. Rev. D34, 38423845 (1986)

YangMills selfenergy in a class of linear gauges, S.L. Nyeo , Phys. Rev. D36, 2512 (1987)

Renormalization of the twist four operator in the light cone gauge, S.L. Nyeo , Nucl . Phys. B273, 195204 (1986)

Technical aspect in the light cone gauge, G. Leibbrandt and S.L . Nyeo , Phys. Rev. D33, 31353137 (1986)

Oneloop N point functions in the light cone gaguge , G. Leibbrandt and S.L. Nyeo , Z. Phys. C30, 501505 (1986)

Nonlocal BRS counterterms in a physical gauge, G. Leibbrandt , and SuLong Nyeo , Nucl . Phys. B276, 459 (1986)

Renormalization questions in the lightcone gauge, A. Andrasi G. Leibbrandt and S.L. Nyeo , Nucl . Phys. B276, 445 (1986)

Two loop Feynman integrals in the physical light cone gauge, G. Leibbrandt and S.L. Nyeo , J. Math. Phys. 27, 627 (1986)

Generalized ward identity for the quark selfenergy and the quark quarkgluon vertex in the lightfront cone gauge. G. Leibbrandt and S.L. Nyeo , Phys. Lett . B140, 417 (1984).

Chilong Lin, ChiaChu Chen, and Chiener Lee , Phys. Rev. D58, 075009 (1998),

Chilong Lin, Chiener Lee, YeouWei Yang, Chinese J. Phys. 32, 41 (1994),

Chilong Lin, Chiener Lee and YeouWei Yang, Phys. Rev. D50, 558 (1994),

JiunMing Hsu, YeouWei Yang and Chiener Lee, Prof. Natl. Sci. Counc . ROC( A), 17, 249 (1993)

Chiener Lee, Benjamin Tseng and YeouWei Yang, Mod. Phys. Lett. A6, 20, 1833 (1991),

Chiener Lee , Chilong Lin and YeouWei Yang, 1991, Progress in High Energy Physics, pp.237, published by Elsevier Science Publishing Co.

Chiener Lee , Chilong Lin and YeouWei Yang, Phys. Rev. D42, 2355 (1990).

Massive torsion modes, chiral gravity and the AdlerBell Jackiw anomaly, L. N, Chang and C. Soo , Class. Quant. Grav . 20, 13791388 (2003)

Wave function of the universe and chernsimons perturbation theory, C. Soo , Class. Quant. Grav.19, 10511064 (2002)

Einstein manifolds, abelian instantons , bundle reduction, and the cosmological constant, C. Soo , Class. Quant. Grav.18, 709718 (2001)

AdlerBell Jackiw anomaly, the NiehYan form, vacuum and polarization, C. Soo , Phys. Rev. D59, 045006 (1999)

Quantum field theory with and without conical singularities: block holes with cosmological constant and multihorizon scenario, F.L. Lin and C. Soo , Class. Quant. Grav.16, 551562 (1999)

Invariant regularization of anomalyfree chiral theories, L. N. Chang and C. Soo , Phys. Rev. D55, 24102421 (1997)

The standard model with gravity couplings, L. N. Chang and C. Soo , Phys. Rev. D53, 56825691 (1996)

Selfdual variable positive semidefinite in 4D quantum gravity, C. Soo , Phys. Rev. D52:34843493 (1995)

The Chern Simons invariant as the natural time variable for classical and quantum cosmology, L. Smolin and C. Soo , Nucl . Phys. B449 289316 (1995)

Semiclassical Quantization of Hopf Solitons , W.C. Su , Phys.Lett . B525 (2002) 201204

FaddeevSkyrme Model and Rational Maps, W. C. Su , Chin. J. Phys. 40 (2002) 516525

Abelian Decomposition of Sp( 2N) YangMills Theory, W. C. Su , Phys. Lett . B499 (2001) 275279

Abelian Decomposition of SO( 2N) YangMills Theory, W. C. Su , Eur . Phys. J. C20 (2001) 717721

On the Z_2 Monopole of Spin( 10) Gauge Theories, W. C. Su , Phys.Rev . D57 (1998) 51005107

A Relation between the Anomalous Dimensions and OPE Coefficients in Asymptotic Free Field Theories, H. Sonoda and W. C. Su , Phys.Lett . B392 (1997) 14114

Operator product expansions in twodimensional O( N) nonlinear sigma model, H. Sonoda and W.C. Su , Nucl . Phys. B441, 310336 (1995)

Conformal Covariantization of Moyal Lax Operators, M. H. Tu , N. C. Lee, and Y. T. Chen, J. Phys. A35 (2002) 4375

Topological Field Theory approach to the Generalized Benney Hierarchy, J. H. Chang and M. H. Tu , hepth/0108059

Nonlocal extended conformal algebras associated with the multiconstraint KP hierarchy and its freefield realizations, J. C. Shaw and M. H. Tu , Int. J. Mod. Phys. A13 (1998) 27232737

Canonical gauge equivalence of the sAKNS and sTB hierarchies, J. C. Shaw and M. H. Tu , J. Phys. A31 (1998) 65176523

A note on the gauge equivalence of the ManinRadul and Laberge Mathieu super KdV hierarchies, J. C. Shaw and M. H. Tu , J. Phys. A31 (1998) 48054810

Solving the constrained KP hierarchy by gauge transformations , L . L. Chau , J. C. Shaw and M. H. Tu , J. Math. Phys. 38 (1997) 41284137

Deep Inelastic Structure Functions in LightFront QCD: Radiative Corrections
A. Harindranth , R. Kunda and W. M. Zhang , Phys. Rev. D59 (1999) 094013 
Nonperturbative Description of Deep Inelastic Structure Functions in LightFront QCD, A. Harindranth , R. Kunda and W. M. Zhang, Phys.Rev . D59 (1999) 094012

Radiative Leptonic B Decays in the Light Front Model, C. Q. Geng , C. C. Lih and W. M. Zhang , Phys. Rev. D57 (1998) 56975702

Quark Confinement in LightFront QCD and A WeakCoupling Treatment to Heavy hadrons, W. M. Zhang , hepph/9510428

LightFront Heavy Quark Effective Theory and Heavy Meson Bound States
C. Y. Cheung, W. M. Zhang and G. L. Lin, Phys. Rev. D52 (1995) 29152925 
Heavy Quark Effective Theory on the Light Front, W. M. Zhang , G. L. Lin and C. Y. Cheung, Int. J. Mod. Phys. A11 (1996) 32973306

LightFront Dynamics and LightFront QCD, W. M. Zhang , Chin.J.Phys . 32 (1994) 717808

LightFront QCD: Role of Longitudinal Boundary Integrals, W. M. Zhang and A. Harindranath , Phys. Rev. D48 (1993) 48684880

Residual Gauge Fixing in LightFront QCD, W. M. Zhang and A. Harindranath Phys. Lett . B314 (1993) 223228
Motivations and Aims :
1. One of the main aims of this program is to pool and organize the resources, expertise and experience of the research community of theorists from Chiayi, Tainan and Kaoshiung in Southern Taiwan. This NCTS program and its joint activities will constitute a platform to facilitate and improve interactions, permit frequent exchanges, and induce integration and collaborations among these theorists at a level BEYOND the support provided by individual grants from the National Science Council.
2. Solving important questions in Physics often require the combined efforts and perspectives of scientists of diverse backgrounds and training. The proposed research activities will focus on several significant topics in the physics and mathematics of quantum gauge field theories and differential geometry. The methodologies include invariant regularization methods, operator expansion techniques, lightfront formalism; and the applications of differential geometry and topology to perturbative and nonperturbative phenomena. Potential results include novel soliton solutions, new phenomenological consequences in CP, T and CPT violations, improvements in invariant and gaugeindependent calculations for chiral theories and quarkhadron physics, and clarification of the role of entropy and entanglement in quantum field theory and quantum information science. The proposed gathering of mathematical physicists, quantum field theorists, and phenomenologists will ameliorate the weaknesses of each subgroup and broaden the limited perspective and applicability of results in a particular subdiscipline through the strengths, experience and expertise of other members