Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary m...Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.展开更多
This paper proposes that all Bosons and all Fermions originate from even more elementary constituents, which called Spin Angular Momentum Vacuum (SAMV). SAMV is filled with Primitive Spin Particles (PSP). The total sq...This paper proposes that all Bosons and all Fermions originate from even more elementary constituents, which called Spin Angular Momentum Vacuum (SAMV). SAMV is filled with Primitive Spin Particles (PSP). The total square spin angular momentum of each PSP is negative, less than zero. Those PSP labeled by index ?of Casimir Operator, are called Vacuum Spin Particle (VSP), which could be contracted into so-called Vacuum Bubbles (VB). VB are identical bubbles, are 'sub-observable physical quantities'. VB are paired up into Vacuum Bubble Pair VBP. VSP ωj(or ω+,ω-) results from Self-identical vacuum bubble interaction ?through the zero order Phase Transition PT. When the 1st, 2nd, 3rd,... order PT of VBP occur, ?then VBP turn into Bosons and Fermions, excited out of sea level of SAMV ocean.展开更多
This paper offers concrete spin matrix forms of 0h spin zero particle, and shows the existent of the spin interactions among 0h spin zero particles. It is obviously hoping to approach, on the most comprehensive level,...This paper offers concrete spin matrix forms of 0h spin zero particle, and shows the existent of the spin interactions among 0h spin zero particles. It is obviously hoping to approach, on the most comprehensive level, to understand what really Higgs Boson is and what role-play Higgs Boson is acting in particle physics. As a "particle" of gravitational force, the spin interaction between 0h spin zero particle (Higgs Boson) and 2h spin particle (Graviton) is given, which maybea way that people would find Graviton in future.展开更多
Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we de...Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm （｜z｜^2） and its generalized generating function formula. A series of recursive relations regarding to L^ρm （｜z｜^2） are also deduced in the context of the Fock representation by algebraic method.展开更多
We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±,...We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.展开更多
Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and ...Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.展开更多
A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum stati...A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions.展开更多
Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the gravito...Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the graviton as the corresponding particle, and Dirac waves with the electron as the corresponding particle. All these theories are stand-alone theories having nothing in common. The outstanding problem is a unified theory of particles and fields. In this paper, we discuss a unified geometrical theory of fields and particles.展开更多
基金The authors would like to thank Prof. Y.D. Zhang for selfless helps and valuable discussions.
文摘Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.
文摘This paper proposes that all Bosons and all Fermions originate from even more elementary constituents, which called Spin Angular Momentum Vacuum (SAMV). SAMV is filled with Primitive Spin Particles (PSP). The total square spin angular momentum of each PSP is negative, less than zero. Those PSP labeled by index ?of Casimir Operator, are called Vacuum Spin Particle (VSP), which could be contracted into so-called Vacuum Bubbles (VB). VB are identical bubbles, are 'sub-observable physical quantities'. VB are paired up into Vacuum Bubble Pair VBP. VSP ωj(or ω+,ω-) results from Self-identical vacuum bubble interaction ?through the zero order Phase Transition PT. When the 1st, 2nd, 3rd,... order PT of VBP occur, ?then VBP turn into Bosons and Fermions, excited out of sea level of SAMV ocean.
文摘This paper offers concrete spin matrix forms of 0h spin zero particle, and shows the existent of the spin interactions among 0h spin zero particles. It is obviously hoping to approach, on the most comprehensive level, to understand what really Higgs Boson is and what role-play Higgs Boson is acting in particle physics. As a "particle" of gravitational force, the spin interaction between 0h spin zero particle (Higgs Boson) and 2h spin particle (Graviton) is given, which maybea way that people would find Graviton in future.
基金supported by the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm （｜z｜^2） and its generalized generating function formula. A series of recursive relations regarding to L^ρm （｜z｜^2） are also deduced in the context of the Fock representation by algebraic method.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)the Key Project of Natural Science Fund of Anhui Province,China(Grant No.KJ2013A261)
文摘We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.
文摘Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.
基金Project supported by the National Natural Science Foundation of China (Grant No 10874142)
文摘A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions.
文摘Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the graviton as the corresponding particle, and Dirac waves with the electron as the corresponding particle. All these theories are stand-alone theories having nothing in common. The outstanding problem is a unified theory of particles and fields. In this paper, we discuss a unified geometrical theory of fields and particles.
