真空中两个点电荷间电势为零的点及其产生的场强

以真空中的两个点电荷为研究对象,讨论了空间坐标系下电势为零的点所形成的轨迹,以及电势为零的点的场强大小及方向;并通过MATLAB进行数值模拟,验证了结论的正确.总结了空间场强求解的一般方法和要点,明确了场强的空间分布性.     

Topology and zero modes in the SU(2) lattice gauge vacuum

Evidence is presented that the Atiyah-Singer index theorem is effectively restored on the lattice for numerically accessible values of the lattice spacing (corresponding to β 4/g² ⩾2.4). It is shown explicitly how topological lattice artifacts decouple from the long-distance fermionic physics. Evidence is presented that while the spontaneous breaking of chiral symmetry does receive contributions of a topological origin, these are not the only contributions.     

Algebraic quantization of systems with a gauge degeneracy

Systems with a gauge degeneracy are characterized either by supplementary conditions, or by a set of generators of gauge transformations, or by a set of constraints deriving from Dirac's canonical constraint method. These constraints can be expressed either as conditions on the field algebra , or on the states on . In aC*-algebra framework, we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra . This factor algebra, , is free of state conditions. In this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions. The connection between states on and states on is investigated further within this framework, as is also the set of transformations which are compatible with the set of constraints. It is also shown that not every set of constraints can give rise to a nontrivial system. Finally as an example, the abstract theory is applied to the electromagnetic field, and this treatment can be generalized to all systems of bosons with linear constraints. The question of dynamics is not discussed.     

Parameter representation of average potential energy of zero point vibrations

The variation of contributions to the average vibrational potential energy with a parameter characterizing the force field has been mapped for some twenty-three bent symmetrical XY₂ systems. Simple and physically significant criteria for the calculation of extremely reliable harmonic force fields are found to emerge from this study. For nonhydrides minimization of the main average bending energy contribution f_ασ_α and for hydrides minimization of the quantity f_ασ_α + 2f_rασ_rα yield excellent force fields in agreement with standard force fields fixed with the help of additional experimental data.     

Charge quantization and vacuum degeneracy in two dimensions

The “chiral limit” of quantum electrodynamics in (1 + 1) dimensions exhibits vacuum degeneracy only if the charges are quantized.     

Finsler gauge transformations and general relativity

The theory of gauge transformations in Finsler space is applied to general relativity. It is seen that the transformations produce new metrics which correspond to the introduction of physical fields. The geodesic equation in the transformed space is equivalent to the equation of motion in the original space where the field is included by a force term. An example is given of a transformation and resulting metric in which the electromagnetic potential is related to parameters of the gauge transformation rather than to gauge potentials. This implies that the electromagnetic field corresponds to a connection instead of a curvature. Another example is given which shows how Weyl or conformal transformations are related to a class of the gauge transformations.     

Moving frame transport and gauge transformations

An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed.     

On zero modes and gauge fixing in light-cone quantized gauge theories

It is shown that regularistation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.

     

A thermodynamically consistent quasi-particle model without temperature-dependent infinity of the vacuum zero point energy

In this Letter, an improved quasi-particle model is presented. Unlike the previous approach of establishing quasi-particle model, we introduce a classical background field (it is allowed to depend on the temperature) to deal with the infinity of thermal vacuum energy which exists in previous quasi-particle models. After taking into account the effect of this classical background field, the partition function of quasi-particle system can be made well-defined. Based on this and following the standard ensemble theory, we construct a thermodynamically consistent quasi-particle model without the need of any reformulation of statistical mechanics or thermodynamical consistency relation. As an application of our model, we employ it to the case of (2+1)$(2+1)$ flavor QGP at zero chemical potential and finite temperature and obtain a good fit to the recent lattice simulation results of Borsányi et al. A comparison of the result of our model with early calculations using other models is also presented. It is shown that our method is general and can be generalized to the case where the effective mass depends not only on the temperature but also on the chemical potential.     

Mass of the fundamental fermion and degeneracy of the vacuum

Within the framework of the Heisenberg variant of the unified nonlinear spinor theory of elementary particles an attempt is made to calculate the mass of the fundamental fermion (nucleon). The guiding principle is the notion of the existence of a relation between the helicity properties of particles and their masses. In this case it proves necessary to take into account the possibility of degeneracy of the vacuum of the system of interacting fields in certain quantum numbers, A program is outlined for constructing a realistic scheme of elementary particles to include their Isotropic and strange properties. The possibility of eliminating divergences from the nonlinear theory, while preserving its applicability, by means of a somewhat modified perturbation theory is briefly discussed.The author is grateful to Professor D. Ivanenko for his constant interest and helpful advice.     

Fields,observables and gauge transformations II

We wish to study the construction of charge-carrying fields given the representation of the observable algebra in the sector of states of zero charge. It is shown that the set of those covariant sectors which can be obtained from the vacuum sector by acting with localized automorphisms has the structure of a discrete Abelian group. An algebra of fields can be defined on the Hilbert space of a representation of the observable algebra which contains each of the above sectors exactly once. The dual group of acts as a gauge group on in such a way that is the gauge invariant part of is made up of Bose and Fermi fields and is determined uniquely by the commutation relations between spacelike separated fields.     

Spontaneous symmetry breaking and constant gauge transformations

Symmetry breaking solutions of several model theories are investigated with the result that constant gauge transformations of the fields describing zero mass Goldstone particles are responsible for the formal possibility of the spontaneous symmetry breaking.

     

Fields,observables and gauge transformations I

Starting from an algebra of fields and a compact gauge group of the first kind , the observable algebra is defined as the gauge invariant part of . A gauge group of the first kind is shown to be automatically compact if the scattering states are complete and the mass and spin multiplets have finite multiplicity. Under reasonable assumptions about the structure of it is shown that the inequivalent irreducible representations of (sectors) which occur are in one-to-one correspondence with the inequivalent irreducible representations of and that all of them are strongly locally equivalent. An irreducible representation of satisfies the duality property only if the sector corresponds to a 1-dimensional representation of . If is Abelian the sectors are connected to each other by localized automorphisms.On leave of absence from Instituto di Fisica G. Marconi, Università di Roma.     

The gauge transformations of the Schwinger model

We determine the group of implementable local gauge transformations of massless quantum electrodynamics in two space-time dimensions in the covariant Landau gauge. It splits into an infinite discrete set of disjoint classes. The unitary operators representing the implementable gauge transformations are constructed explicitly. A subset of these operators does not reduce to multiples of the identity in the physical Hilbert space constructed according to the usual rules. The disappearance of the fermionic degrees of freedom is related to this fact. Combined with the properties of the global chiral transformations, it provides a better understanding of the model's vacuum structure.     

Gauge transformations and quantum mechanics II. Physical interpretation of classical gauge transformations

New gauges are introduced. The potentials, vector and scalar, in these gauges are obtained in closed forms by the Green's function method. These closed form solutions are explicity expressed only in terms of the charge and current densities. The physical interpretation is on how potentials propagate from the charge and current densities. The Coulomb gauge and the Lorentz gauge are special cases of a new gauge defined in this paper. It is called the complete α-Lorentz gauge. The scalar potential propagates at speed αc from the charge density for any positive α. When α is one, the usual solutions for the Lorentz gauge are recovered. When α is not one, our results show that, in order to satisfy the requirement that electromagnetic fields be gauge invariant and in order to conform to Maxwell's interpretation that electromagnetic fields propagate at speed c from the charge and current densities (we only consider the vacuum), the vector potential must contain two mathematically and physically independent gradient components. Furthermore, one such component must propagate at speed αc while the other must at speed c from charge and current densities. Our discussions on the Coulomb gauge are based on the results obtained by letting α go to (positive) infinity. Guided by Maxwell's interpretation, we introduce a new decomposition of the vector potential in the Lorentz gauge into a longitudinal and a transverse component. For an arbitrary charge and current distribution, it is shown that the transverse component will generate all the fields only in the radiation zone. However, for a point charged particle, the transverse component only generates the “free fields”everywhere in the instantaneous rest frame of the charged particle.     

Point transformations and renormalization in the unitary gauge

It is shown by means of a model that the renormalization and unitary gauges can be connected by a point transformation, and this fact is used to construct a formal proof of renormalization in the unitary gauge. The formal proof is then verified by demonstrating that for a fourth-order on-shell scattering process the S-matrix calculated directly in the unitary gauge is exactly equal to that calculated in the renormalization gauge. The calculation is refined to the point where it becomes purely graphical and this allows one to see by inspection how the cancellation of divergences occurs in the unitary gauge. The model considered here is Abelian, but it will be generalized to the non-Abelian case subsequently.     

The structure of the gauge theory vacuum

The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.     

Invariance of fermion determinant under large gauge transformations

We argue that in the perturbative framework the natural symmetry of the fermionic determinant is the perturbative gauge transformation (p.g.t.) which differs from the usual gauge transformation of the effective action through the absence of terms independent of the coupling constant. Calculated in a non-perturbative framework appropriate for large gauge function, the sum of these latter terms vanish. In three dimensions the invariance of the full fermion determinant under large gauge transformations is thus ensured due to the invariance under p.g.t. of the Chern-Simons term arising in some perturbative regularisations.