The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle ei...The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle eigenfunction, we obtain continuous spectrum of these potentials by means of their shape invariance symmetry in an algebraic method.展开更多
This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP...This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP>?</SUP> for a charged particle in classical electromagnetic field, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Different methods correspond to different unitary operators which satisfy the above-mentioned principle.展开更多
The Higgs decay H →γγ due to the virtual W-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method, which is realized in the fourd...The Higgs decay H →γγ due to the virtual W-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method, which is realized in the fourdimensional space-time without changing original theory. Though the one-loop amplitude of H →γγ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level, it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined. As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance, we explicitly show the absence of decoupling in the limit Mw /MH → 0 and obtain a result agreeing exactly with the earlier one in the literature. We then clarify the discrepancy of the earlier result from the recent one obtained by R. Castmans, S.L. Wu and T.T. Wu. The advantage of calculation in the unitary gauge becomes manifest in that the non-decoupling arises from the longitudinal contribution of the W gauge boson.展开更多
文摘The shape invariant symmetry of the Trigonometric Rosen-Morse and Eckart potentials has been studied through realization of so（3） and so（2, 1） Lie algebras respectively. In this work, by using the free particle eigenfunction, we obtain continuous spectrum of these potentials by means of their shape invariance symmetry in an algebraic method.
文摘This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP>?</SUP> for a charged particle in classical electromagnetic field, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Different methods correspond to different unitary operators which satisfy the above-mentioned principle.
基金Supported by the National Science Foundation of China under Grant Nos. 10821504,10975170the Key Project of the Chinese Academy of Sciences
文摘The Higgs decay H →γγ due to the virtual W-loop effect is revisited in the unitary gauge by using the symmetry-preserving and divergent-behavior-preserving loop regularization method, which is realized in the fourdimensional space-time without changing original theory. Though the one-loop amplitude of H →γγ is finite as the Higgs boson in the standard model has no direct interaction with the massless photons at tree level, it involves both tensor-type and scalar-type divergent integrals which can in general destroy the gauge invariance without imposing a proper regularization scheme to make them well-defined. As the loop regularization scheme can ensure the consistency conditions between the regularized tensor-type and scalar-type divergent irreducible loop integrals to preserve gauge invariance, we explicitly show the absence of decoupling in the limit Mw /MH → 0 and obtain a result agreeing exactly with the earlier one in the literature. We then clarify the discrepancy of the earlier result from the recent one obtained by R. Castmans, S.L. Wu and T.T. Wu. The advantage of calculation in the unitary gauge becomes manifest in that the non-decoupling arises from the longitudinal contribution of the W gauge boson.
