Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

A field configuration closer to the true QCD vacuum

An effective action for QCD at one-loop order, which is real, manifestly Lorentz and gauge invariant and which depends on an infinite family of gauge invariants (tr(F _μν F _μν), tr(F _μν F _μν F _?σ F _?σ),...), is obtained. Moreover, anAnsatz for a vacuum configuration is made, whose corresponding vacuum energy density is lower than the one for the SavvidyAnsatz. Both the cases of pure QCD and of QCD with massless fermions are considered.     

Vacuum of the quantum Yang-Mills theory and magnetostatics

It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling $\text{g}\text{(t), t =}\text{ln}\text{[}\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{)}{}^2\text{μ}{}^4\text{]}$. The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F_μν^a = 0, and ferromagnetism, for which (F_μν^a)² = λ², i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields B_μν subject to the gauge transformation δB_μν = ?_μξ_ν ? ?_νξ_μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.     

The ideal relativistic rotating gas as a perfect fluid with spin

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ_μν. After having obtained the expression of the local spin-dependent phase-space density f(x, p)_στ in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω_μν constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω_μνσ^μν. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t^μ = σ_μνu^ν ≠ 0, in contrast to the common assumption t^μ = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.     

Perturbative QED in terms of gauge invariant fields

A formulation of QED using only gauge invariant fields acting on a physical state space is discussed. The fields are the electromagnetic tensor F_μν and a non-local electron field ψ_f depending on a quadruple {f^μ} of auxiliary functions. The f-ambiguity is physically meaningful: the f^μ contain information on the asymptotic configuration of the electromagnetic field accompanying charged particles. Equations of motion are introduced and solved perturbatively, in the sense that expressions for the Wightman functions of the theory are derived. No information on the commutation relations between the basic fields is needed.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.     

Limitations on the existence of massless composite states

Massless particles represented by the fields with mixed spinor indices of SL(2,C) are generally shown to be forbidden in covariant field theory under the assumptions of positivity and covariiance alone. This remains true also in gauge theory (in which a negative metric appears) as far as the particles are gauge invariant. This in particular implies that any dynamical “gauge-type particle” (such as vector A_μ, Rarita-Schwinger ψ_μ etc.) cannot appear unless the system has a corresponding local invariance from the outset.     

The energy-momentum tensor in scalar and gauge field theories

A previous study of the energy-momentum tensor in ?⁴ theory and spontaneously broken non-Abelian gauge field theories is extended here to show finiteness to all orders in perturbation theory. Divergences of Green's functions Γ_μν^(j) (q; p₁, …, p_j) involving the energy-momentum tensor θ_μν and j particle fields are removed by counterterms of the ordinary Lagrangian plus a renormalization of the coefficient of the Callan-Coleman-Jackiw improvement term in θ_μν. Physically the extra renormalization means that the mean square “mass radius” of elementary spin zero particles must be specified from experiment.     

Gravity and gauge: A new perspective

Realization of the Poincaré groupP ₁₀ as a subgroup ofGL(5,R) that maps a 4-dimensional affine set into itself has been shown to lead to a direct Yang-Mills gauging process. This paper discusses the differences between direct gauge theory forP ₁₀ and previously published works. These differences are fundamental, both physically and mathematically, and lead to marked departures from previous concepts and interpretations. The translation subgroup is correctly gauged; the metric structure and metric compatibility are derived from the gauging process rather than assumed; spin structures are automatically incorporated in a consistent manner; the local holonomy group is shown to be the component of the Lorentz group connected to the identity; the geometric analog of Yang-Mills minimal coupling precludes dependence of the free gauge field Lagranian on torsion; and the theory reduces exactly to general relativity when the momentumenergy complex is symmetric and all matter fields are spin-free. Gravitational effects on neutral test particles are shown to arise from the compensating 1-forms for local action of Lorentz boosts. The compensating 1-forms for local action of the translation subgroup may be interpreted as space-time dislocations, while the compensating 1-forms for the rotation subgroup can be viewed as space-time disclinations. Unfortunately, there are no clear physical meanings that can be ascribed to space-time dislocations or disclinations.     

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant G_f ? 10³⁸G_N (G_N being the Newtonian constant) and a cosmological term λ_f ?;_μν (?;_μν is strong gravity metric and λ_f ～ 10²⁸ cm^? is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature ～10^?14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length ～2 × 10^?14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-$\text{1}\text{2}$ particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

Fluid-dynamical description of nuclear collective excitations

The role of antisymmetric tensor fields in the gauging of groups is related to theorems on cohomology theory, and Cartan integrable systems are discussed. Examples are given. Various possibilities to gauge d = 11 supergravity by decontracting its underlying group are considered. In particular the simple supergroups Osp (1 | 64) and SU(32 | 1) yield a negative result, but a certain non-semisimple supergroup containing Osp (1 | 32) is proposed as a viable candidate. The corresponding action would no longer contain the 3-index photon A_μν?, but instead a second spin $\text{3}\text{2}$ field η_μ and boson fields $\text{B}{}_{\mathrm{\mu }}{}^{\mathrm{a1a2}}$ and $\text{B}{}_{\mathrm{\mu }}{}^{\mathrm{a1\dots a5}}$. A first order formalism for d = 11 is presented. It is to be used for an improved form of dimensional reduction.     

The electromagnetic string with spin

The relations betweeb a field F_μν^M satisfying the usual Maxwell equations and a field F_μν^D satisfying the symmetric Maxwell-Dirac equations, and the singular potential solving both of these is given. The action principle is formulated in both forms and the reality of the string is shown. A string with spin is constructed by placing electric charges at its end-points. The motion and interactions of the string, the relation between flux and angular momentum quantization and the passage to two-body Hamiltonians are examined.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.