In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B^n is mixing and generically 5-chaotic with any 0 < δ < 2 for each positive integer n.Besides,by using...In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B^n is mixing and generically 5-chaotic with any 0 < δ < 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A:Math.Theor.,2011,44:505101],the authors obtain that the principal measure of B^n is equal to 1 for each positive integer n.展开更多
We derive the basic canonical brackets amongst the creation and annihilation operators for a two(1 + 1)-dimensional(2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field(Aμ) is coupl...We derive the basic canonical brackets amongst the creation and annihilation operators for a two(1 + 1)-dimensional(2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field(Aμ) is coupled with the fermionic Dirac fields(ψ andˉψ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries(and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta(corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries(and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.展开更多
基金supported by YBXSZC20131046the Scientific Research Fund of Sichuan Provincial Education Department under Grant No.14ZB0007
文摘In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B^n is mixing and generically 5-chaotic with any 0 < δ < 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A:Math.Theor.,2011,44:505101],the authors obtain that the principal measure of B^n is equal to 1 for each positive integer n.
基金the financial support from CSIR and UGC, New Delhi, Government of India, respectively
文摘We derive the basic canonical brackets amongst the creation and annihilation operators for a two(1 + 1)-dimensional(2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field(Aμ) is coupled with the fermionic Dirac fields(ψ andˉψ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries(and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta(corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries(and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.
