This paper attempts to propose a grand unified guiding principle of gauge fields from the mathematical and physical picture of fiber bundles: it is believed that our universe may have more fundamental interactions tha...This paper attempts to propose a grand unified guiding principle of gauge fields from the mathematical and physical picture of fiber bundles: it is believed that our universe may have more fundamental interactions than the four fundamental interactions, and the gauge fields of these fundamental interactions are just a unified gauge potential on the fiber bundle manifold or the components connected to the bottom manifold, that is, our universe;these components can meet the transformation of gauge potential, and even can be transformed from a fundamental interaction gauge potential to another fundamental interaction gauge potential, and can be summarized into a unified equation, namely the expression of the generalized gauge equation, corresponding to the gauge transformation invariance;so gauge transformation invariance is a necessary condition to unify field theory, but quantization of field is not a necessary condition;the four (or more) fundamental interaction fields of the universe are unified into a universal gauge field defined by the connection of the principal fiber bundle on the cosmic base manifold.展开更多
Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and m...Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons.展开更多
In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar ...In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.展开更多
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently.The standard model is defined perturbatively and describes all elementary particles(ex...The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently.The standard model is defined perturbatively and describes all elementary particles(except gravitons)very well.However,for a long time,we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory.Here we propose a way to give a modified standard model(with 48 two-component Weyl fermions)a non-perturbative definition by embedding the modified standard model into an SO(10)chiral gauge theory.We show that the SO(10)chiral gauge theory can be put on a lattice(a 3D spatial lattice with a continuous time)if we allow fermions to interact.Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume.More generally,using the defining connection between gauge anomalies and the symmetry-protected topological orders,one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension.展开更多
Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are ...Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.展开更多
The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algeb...The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.展开更多
A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary a...A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.展开更多
Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) l...Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional SU(2) theory has only a single, confining phase. The unwanted discontinuity of EP given by the single link trial action, which is used in the earlier variational calculations has been avoided.展开更多
The Faddeev-Jackiw quantization procedure is applied to the gauge invariant version of the linear self-dual constrained theory.The equivalence of the gauge invariant and the gauge noninvariant versions is discussed.
A variational-cumulant expansion method at finite temperature is developed in the lattice gauge theory.The order parameter<L>(the statistical average of the thermal loop)is analytically calculated to the 3rd ord...A variational-cumulant expansion method at finite temperature is developed in the lattice gauge theory.The order parameter<L>(the statistical average of the thermal loop)is analytically calculated to the 3rd order cumulant expansion.The change of<L>=0 to<L>≠0 clearly shows the existence of a deconfine phase transition of 2nd order in agreement with the latest Monte Carlo simulations.展开更多
The variational method has been applied to investigating the phase diagrams of the two parameter actions containing TrU(P)^(3) term in SU(2)lattice gauge theory.The result is in agreement with that obtained by Monte C...The variational method has been applied to investigating the phase diagrams of the two parameter actions containing TrU(P)^(3) term in SU(2)lattice gauge theory.The result is in agreement with that obtained by Monte Carlo simulations.This can be helpful to understand the mechanism of the phase transitions.展开更多
Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implement...Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.展开更多
The standard theory of general relativity (GR) can be written in a form proposed by Eddington using the parametric representation of the metric tensor. In this paper, the equations of the standard theory of GR using t...The standard theory of general relativity (GR) can be written in a form proposed by Eddington using the parametric representation of the metric tensor. In this paper, the equations of the standard theory of GR using the parametric representation are first developed. Afterwards, the fundamental ideas of a new type of abelian self-interacting gauge theory are presented. Finally, it is shown that the gauge field equations of this new theory are identical to the parametric form of Einstein’s equations of general relativity. It is concluded that classical gravity can be described either by the usual theory of GR in a curved space-time or, alternatively as a self-interacting gauge theory independent of the dynamics of space-time.展开更多
Inertial and gravitational mass or energy momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dime...Inertial and gravitational mass or energy momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The gauge-fixed action and the path integral measure occurring in the generating functional for the quantum Green functions of the theory are shown to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting the corresponding quantum effective action is established. This equation limits the infinite parts of the quantum effective action to have the same form as the gauge-fixed Lagrangian of the theory proving its spacetime renormalizability. The inner space integrals occurring in the quantum effective action which are divergent due to the gauge group’s infinite volume are shown to be regularizable in a way consistent with the symmetries of the theory demonstrating as a byproduct that viable quantum gauge field theories are not limited to finite-dimensional compact gauge groups as is commonly assumed.展开更多
In this paper, we have proposed the theory of gravity gauge, and the gravity theory has been introduced into quantum field theory. We have further given the tensor equation of gravity field in the flat space, and foun...In this paper, we have proposed the theory of gravity gauge, and the gravity theory has been introduced into quantum field theory. We have further given the tensor equation of gravity field in the flat space, and found the gravity field equation is the Lorentz covariant and gauge invariant. The gravity theory can be quantized and can be unified with the electroweak and strong interaction at a new gauge group .展开更多
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacet...The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.展开更多
We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield f...We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BRST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.展开更多
文摘This paper attempts to propose a grand unified guiding principle of gauge fields from the mathematical and physical picture of fiber bundles: it is believed that our universe may have more fundamental interactions than the four fundamental interactions, and the gauge fields of these fundamental interactions are just a unified gauge potential on the fiber bundle manifold or the components connected to the bottom manifold, that is, our universe;these components can meet the transformation of gauge potential, and even can be transformed from a fundamental interaction gauge potential to another fundamental interaction gauge potential, and can be summarized into a unified equation, namely the expression of the generalized gauge equation, corresponding to the gauge transformation invariance;so gauge transformation invariance is a necessary condition to unify field theory, but quantization of field is not a necessary condition;the four (or more) fundamental interaction fields of the universe are unified into a universal gauge field defined by the connection of the principal fiber bundle on the cosmic base manifold.
文摘Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons.
文摘In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.
基金This research is supported by NSF Grant No.DMR-1005541,NSFC 11074140,and NSFC 11274192。
文摘The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently.The standard model is defined perturbatively and describes all elementary particles(except gravitons)very well.However,for a long time,we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory.Here we propose a way to give a modified standard model(with 48 two-component Weyl fermions)a non-perturbative definition by embedding the modified standard model into an SO(10)chiral gauge theory.We show that the SO(10)chiral gauge theory can be put on a lattice(a 3D spatial lattice with a continuous time)if we allow fermions to interact.Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume.More generally,using the defining connection between gauge anomalies and the symmetry-protected topological orders,one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension.
基金Project supported by the Key Laboratory Project of Computational Physics of National Defense Science and Technology of China(Grant No.6142A05180401)the National Key Program for S&T Research and Development of China(Grant Nos.2019YFA0307700 and 2016YFA0401100)the National Natural Science Foundation of China(Grant Nos.11847307,11425414,11504215,11774361,and 11874246).
文摘Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.
文摘The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.
基金Project supported by the National Natural Science Foundation of China (Grant No 10475036)
文摘A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.
文摘Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional SU(2) theory has only a single, confining phase. The unwanted discontinuity of EP given by the single link trial action, which is used in the earlier variational calculations has been avoided.
文摘The Faddeev-Jackiw quantization procedure is applied to the gauge invariant version of the linear self-dual constrained theory.The equivalence of the gauge invariant and the gauge noninvariant versions is discussed.
基金supported in part by the Science Fund of The Chinese Academy of Sciences and by The Foundat ion of Zhongshan University Advanced Research Center.
文摘A modified hamiltonian of lattice gauge theory including 2-plaquette,interaction has been studied.We have found the exact ground state of the theory.
基金The work was supported by the National Science Fund of China.
文摘A variational-cumulant expansion method at finite temperature is developed in the lattice gauge theory.The order parameter<L>(the statistical average of the thermal loop)is analytically calculated to the 3rd order cumulant expansion.The change of<L>=0 to<L>≠0 clearly shows the existence of a deconfine phase transition of 2nd order in agreement with the latest Monte Carlo simulations.
基金supported in part by the Science Fund of the Chinese Academy of Science。
文摘The variational method has been applied to investigating the phase diagrams of the two parameter actions containing TrU(P)^(3) term in SU(2)lattice gauge theory.The result is in agreement with that obtained by Monte Carlo simulations.This can be helpful to understand the mechanism of the phase transitions.
基金supported by China Postdoctoral Science Foundation(Grant No.2020T130643)the Fundamental Research Funds for the Central Universities,and the National Natural Science Foundation of China(Grant No.12047554)+5 种基金support from the National Key Research and Development Program of China(Grant No.2016YFA0300502)the Research Grants Council of Hong Kong SAR China(Grant No.17303019)support from the National Key R&D Program of China(Grant Nos.2016YFA0302104 and 2016YFA0300600)the National Natural Science Foundation of China(Grant Nos.11774406 and 11934018)Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)Beijing Academy of Quantum Information Science(Grant No.Y18G07)。
文摘Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.
文摘The standard theory of general relativity (GR) can be written in a form proposed by Eddington using the parametric representation of the metric tensor. In this paper, the equations of the standard theory of GR using the parametric representation are first developed. Afterwards, the fundamental ideas of a new type of abelian self-interacting gauge theory are presented. Finally, it is shown that the gauge field equations of this new theory are identical to the parametric form of Einstein’s equations of general relativity. It is concluded that classical gravity can be described either by the usual theory of GR in a curved space-time or, alternatively as a self-interacting gauge theory independent of the dynamics of space-time.
文摘Inertial and gravitational mass or energy momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The gauge-fixed action and the path integral measure occurring in the generating functional for the quantum Green functions of the theory are shown to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting the corresponding quantum effective action is established. This equation limits the infinite parts of the quantum effective action to have the same form as the gauge-fixed Lagrangian of the theory proving its spacetime renormalizability. The inner space integrals occurring in the quantum effective action which are divergent due to the gauge group’s infinite volume are shown to be regularizable in a way consistent with the symmetries of the theory demonstrating as a byproduct that viable quantum gauge field theories are not limited to finite-dimensional compact gauge groups as is commonly assumed.
文摘In this paper, we have proposed the theory of gravity gauge, and the gravity theory has been introduced into quantum field theory. We have further given the tensor equation of gravity field in the flat space, and found the gravity field equation is the Lorentz covariant and gauge invariant. The gravity theory can be quantized and can be unified with the electroweak and strong interaction at a new gauge group .
文摘The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.
文摘We present a brief review of the cohomological solutions of self-coupling interactions of the fields in the free Yang-Mills theory. All consistent interactions among the fields have been obtained using the antifield formalism through several order BRST deformations of the master equation. It is found that the coupling deformations halt exclusively at the second order, whereas higher order deformations are obstructed due to non-local interactions. The results demonstrate the BRST cohomological derivation of the interacting Yang-Mills theory.