On the Gauge Invariance of The Transition Probability of A Charged Particle in Electromagnetic Field

This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H0, into true physical quantity UH0U? 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.

Gauge invariance and quantization applied to atom and nucleon internal structure

The prevailing theoretical quark and gluon momentum,orbital angular momentum and spin operators,satisfy either gauge invariance or the corresponding canonical commutation relation,but one never has these operators which satisfy both except the quark spin.The conflicts between gauge invariance and the canonical quantization requirement of these operators are discussed.A new set of quark and gluon momentum,orbital angular momentum and spin operators,which satisfy both gauge invariance and canonical momentum and angular momentum commutation relation,are proposed.To achieve such a proper decomposition the key point is to separate the gauge field into the pure gauge and the gauge covariant parts.The same conflicts also exist in QED and quantum mechanics,and have been solved in the same manner.The impacts of this new decomposition to the nucleon internal structure are discussed.

An Outline of the Grand Unified Theory of Gauge Fields

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.

Simple formula for the ionization rate of diatomic molecules in an intense laser field using the velocity gauge

We derive a general ionization rate formula for the system of diatomic molecules in the velocity gauge. A more concise expression of the photoionization rate in the tunnel region is obtained for the first time. Comparisons are made among the different versions of strong-field approximation. The numerical study shows that the ionization rate in the velocity gauge is underestimated by a few orders compared with that in the length gauge. Our simple formula of ionization rate may provide an insight into the ionization mechanism for the system of diatomic molecules.

The SO(3,1)-Gauge Invariant Approach to Fermions on Rindler Spacetime

We try to explicitly derive the Lorentz-gauge covariant Dirac equation, in terms of pseudo-orthonormal bases, on Rindler spacetime and to work out, with all the necessary coefficients, the respective closed-form solutions, in both Dirac and Weyl representations.

Completing Einstein’s Spacetime

The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.

Gauge invariant perturbations of general spherically symmetric spacetimes

In this paper,the gauge choices in general spherically symmetric spacetimes are explored.In particular,we construct the gauge invariant variables and the master equations for both the Detweiler easy gauge and the Regge-Wheeler gauge,respectively.The particular cases for l=0,1 are also investigated.Our results provide analytical calculations of metric perturbations in general spherically symmetric spacetimes,which can be applied to various cases,including the effective-one-body problem.A simple example is presented to show how the metric perturbation components are related to the source perturbation terms.

Expansion of EYM amplitudes in gauge invariant vector space

Motivated by the problem of expanding the single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes,we present an alternative expansion formula in gauge invariant vector space.Starting from a generic vector space consisting of polynomials of momenta and polarization vectors,we define a new sub-space as a gauge invariant vector space by imposing constraints on the gauge invariant conditions.To characterize this sub-space,we compute its dimension and construct an explicit gauge invariant basis from it.We propose an expansion formula in this gauge invariant basis with expansion coefficients being linear combinations of the Yang-Mills amplitude,manifesting the gauge invariance of both the expansion basis and coefficients.With the help of quivers,we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm using several examples.

H→γγ:a comment on the indeterminacy of non-gauge-invariant integrals

We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al. [1, 2]. The reasons for why this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon Rξ-gauge calculations with four-dimensional gauge-breaking regulators, allows us to recover the well known H→γγ result. However we show that in the particular case of the unitary gauge, the indeterminacy cannot be tackled in the same way. The combination of the unitary gauge with a cutoff regularization scheme turns out to be non-predictive.

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.

On the Uniqueness of Ghost-Free Special Gravity

Special gravity refers to interacting theories of massless gravitons in Minkowski space-time which are invariant under the abelian gauge invariance hab → hab ＋ δ（axb） only. In this article we determine the most general form of special gravity free of Ostrogradski ghosts, meaning its equation of motion is of at most second order. Together with the recent works, this result could be helpful in formulating proofs of General Relativity as the unique physical theory of self-interacting massless gravitons. We also study how to construct gauge invariant couplings to matter fields.

Photoproduction reactionγn→K^(*0)∧in an effective Lagrangian approach

In our previous work[Phys.Rev.C 101,014003(2020)],the photoproduction reactionγp→K^(*+)Λwas investigated within an effective Lagrangian approach.The reaction amplitudes were constructed by including the t-channel K,K^(*),and k exchanges,u-channelΛ,∑,and∑^(*)exchanges,s-channel N,N(2000)5/2^(+),and N(2060)5/2^(-)exchanges,and interaction current.The data on the differential cross sections and spin density matrix elements were described simultaneously.In this study,we investigate the photoproduction reactionγn→K^(*0)Λbased on the same reaction mechanism as that ofγp→K^(*+)Λto obtain a unified description of the data forγp→K^(*+)Λandγn→K^(*0)Λwithin the same model.All hadronic coupling constants,form factor cutoffs,and the resonance masses and widths in the present calculations remain the same as in our previous work forγp→K^(*+)Λ.The available differential cross-section data forγn→K^(*0)Λare well reproduced.Further analysis shows that the cross sections ofγn→K^(*0)Λare dominated by the contributions of the t-channel K exchange,while the s-channel N(2000)5/2+and N(2060)5/2-exchanges also provide considerable contributions.

Photoproductionγp→K^(+)Λ(1690)in an effective Lagrangian approach

A gauge-invariant model is constructed for theγp→K^(+)Λ(1690)reaction within a tree-level effective Lagrangian approach to understand the underlying production mechanisms and study the resonance contributions in this reaction.In addition to the t-channel K and K^(∗)exchanges,s-channel nucleon exchange,and interaction current,the s-channel nucleon resonance exchanges are included in constructing the reaction amplitudes to describe the data.It is found that the contributions from the s-channel N(2570)5/2^(−)exchange are required to describe the most recently measured total cross-section data forγp→K^(+)Λ(1690)from the CLAS Collaboration.Further analysis indicates that the interaction current dominates the γ p→K^(+)Λ(1690)reaction near the threshold as a result of gauge invariance.The t-channel K exchange contributes significantly,while the contributions from the t-channel K^(∗)exchange and s-channel nucleon exchange are ultimately negligible.The contributions from the s-channel N(2570)5/2^(−)exchange are found to be responsible for the bump structure shown in the CLAS total cross-section data above the center-of-mass energy W≈2.7 GeV.The predictions of the differential cross sections forγp→K^(+)Λ(1690)are presented and discussed,which can provide theoretical guidance for future experiments.

Education for Sustainability:Lessons from Living Systems Governance

To survive that is to eat and not to be eaten. Whatever its spatial and temporal level of organisation, every living system owns 7 invariant capacities(the gauge invariance paradigm). Emerging by embedments and juxtapositions of previous systems, every living system-of-systems is both dependent and independent from its new global level of organisation and past and present local situations of emergence. Mass growth governs growth phase duration. Local actors, modules of past, present and new modules of modules become mutually integrated(percolation process) into a new Whole through their merging into an ARMSADA(Association for the Reciprocal and Mutual Sharing of Advantages and DisAdvantages). Reversely(systemic constructal law) the global Whole is integrating the local parceners. Whatever the organisation level, the living systems obey the same principle of evolution and emergence, the volume and time of generation of the adult system obey a correlation: The mass controlled duration of acquisition of the reproductive capacity and the volume at its acquisition are linked by a 3/2 exponent power law. This dynamic fractal law is invariant, between and within levels of organisation. Brownian motion is the basic phenomenon of growth control: Matter and energy are exchanged at a constant flow rate. A Pareto-like relationship governs limits and limitations: Mutual survival depends on reciprocal limitations, through interactive feedbacks, for the best and for the worst. To survive that is to transform disadvantages into advantages and to avoid advantages turn to disadvantages.

Massive self-duality solution associated with invariant one-forms

A massive self-duality solution associated with invariant 1-forms is presented. At the zero mass limit the massive self-dual theory of the SO（3） gauge group on 4 dimensions cannot be reduced to that of massless self-duality.In such a case the self-dual connection turns to the flat connection and one cannot obtain a massless theory in such an approach.