| In the nineties of the twentieth century,it is founded that when the open string is fixed at D-brane and interact with NS-NS B field,the string theory at low energy limit will lead to a quantum field theory in noncommutative space-time.Subsequently,people build a noncommutative stadard model based on Weyl-Moyal product.However in the model where the gauge group is not closed in SU(3)x SU(2)×U(1)Lie algebra but in the enveloping algebra,the matter field of noncommutative gauge theory can only be coupled with two gauge fields,and the charge of the noncommutative field is quantized and can only take(+1,0,-1),namely no-go theorem.Seiberg and Witten point out that there is a map between the field in noncommutative space and ordinary space-time,it can solve the no-go theorem’s difficulties.The noncommutative gauge field introduce many new particle vertex beyond the SM,such as γ—γ—γ Lorentz-violating vertex,neutrino-photon vertex etc.The flavor oscillation of the neutrinos shows that the mass scale of neutrino is very tiny,which can not be interpreted in the standard model.The seesaw mechanism introduces the right-handed neutrino with the large mass scale to depress the mass scale of the neutrino.However,there is no obvious evidences for the existence of the right-handed neutrino with the large mass scale.Introducing constant background fields into the noncommutative gauge theory,we first obtain a Hermitian fermion Lagrangian which involves a Lorentz violation ter-m,then we generalize it to a new deformed canonical noncommutation relations for fermion field.Massless neutrino oscillation in the deformed canonical noncommuta-tion relations is analyzed.The restriction of the noncommutative coefficients is also discussed.By comparing with the existing experimental data of conventional neutrino oscillations,the order of noncommutative deformed coefficients is given from different ways.Noncommutative geometry may be an optional way to a quantum gravity,We study the influence of the spacetime noncommutative parameter on the dirac quasinor-mal modes in the noncommutative Schwarzschild blackhole spacetime.In comparison to the commutative Schwarzschild black hole,the numerical results show that oscil-lation frequencies and the magnitude of imaginary part of Dirac quasinormal modes increase.However,it is found that the influence of the spacetime noncommutative parameter on the Dirac quasinormal modes is tiny and negligible.Depending on deformed canonical anti-commutation relations,massless neutri-no oscillation based on Lorentz invariance violation in non-commutative field theory is discussed.It is found that the previous studies about massless neutrino oscillation within deformed canonical anti-commutation relations should satisfy the condition of new Moyal product and new non standard commutation relations.Furthermore,com-paring the Lorentz Invariant Violation parameters A in the previous studies with new Moyal product and new non standard commutation relations,we find that the orders of magnitude of non-commutative parameters(Lorentz invariant Violation parameters A)is not self-consistent.This inconsistency means that the previous studies of Lorentzinvariance violation in non-commutative field theory may not naturally explain mass-less neutrino oscillation.In other words,it should be impossible to explain neutrino oscillation by Lorentz invariance violation in non-commutative field theory.This con-clusion is supported by the latest atmospheric neutrinos experimental results from the Super-Kamiokande Collaboration,which show that no evidence of Lorentz invariance violation on atmospheric neutrinos was observed.The Eigenstate Method has been developed to deduce the fermion propagator with a constant external magnetic field.In general,we find its result is equivalent to other methods and this new method is more convenient,especially when one evaluates the contribution from the infinitesimal imaginary term of the fermion propagator.Using the Eigenstate Method we try to discuss:if the infinitesimal imaginary frequency of fermion propagator in strong magnetic field and Lorentz-violating extension of theminimal SU(3)x SU(2)x SU(1)Standard Model,could have a significant influence on the dynamical mass.When imaginary term of fermion propagator in this model is not trivial,this model gives a corrections to dynamical mass.When one does not consider the influence from imaginary term,there is a another corrections from conventional term.Under both circumstances,chiral symmetry is broken.Identity relations among the transverse parts of various vertex functions involv-ing the vector and the tensor current operators in QED3 theories are derived.At tree level,the normal(longitudinal)Ward-Takahashi identities together with the transverse Ward-Takahashi identities form a complete set of Ward-Takahashi type constraint re-lations for three-point vertex functions.The full vector and tensor vertices at tree level can be expressed in term of the fermion propagators in QED3.At tree level it means that Dyson-Schwinger equation(DSE)can form a closed system for the fermion prop-agators in QED3.In addition,based on the method of computing the curl of vector,axial-vector and the tensor current operator equations,the possible quantum anomaly for the transverse Ward-Takahashi relations in QED3 and QED2 theories is studied.In QED3 theory,the absence of transverse anomalies for both vector and tensor current is verified.In QED2 theory,the transverse WT relation for the axial-vector vertex have an anomalies term.At tree level,We find that the full vector and tensor vertices functions can be expressed in terms of the fermion propagators in QED3.In this case,Dyson-Schwinger equation(DSE)can form a closed system for the fermion propagators,then we can obatin the formal solution of DSE. |
