We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Y...We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Yuan published in CMP(2002),which shows that there are rich KAM tori for a class of Hamiltonian with short range and with linearized operator of pure point spectra.We also present several open problems.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
基金supported by National Natural Science Foundation of China (Grant Nos.11271076 and 11121101)the National Basic Research Program of China (973 Program) (Grant No.2010CB327900)
文摘We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Yuan published in CMP(2002),which shows that there are rich KAM tori for a class of Hamiltonian with short range and with linearized operator of pure point spectra.We also present several open problems.
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.
