The pion form factor within the hidden local symmetry model

We analyze a pion form factor formulation which fulfills the Analyticity requirement within the Hidden Local Symmetry (HLS) Model. This implies an s-dependent dressing of the VMD coupling and an account of several coupled channels. The corresponding function provides nice fits of the pion form factor data from s=-0.25 to s=1 GeV². It is shown that the coupling to has little effect, while improves significantly the fit probability below the mass. No need for additional states like shows up in this invariant-mass range. All parameters, except for the subtraction polynomial coefficients, are fixed from the rest of the HLS phenomenology. The fits show consistency with the expected behaviour of at s=0 up to and with the phase shift data on from threshold to somewhat above the mass. The sector is also examined in relation with recent data from CMD-2. Received: 13 January 2003, Revised: 12 March 2003, Published online: 2 June 2003     

Canonical quantization of the Parisi-Sourlas model

The Parisi-Sourlas model is canonically quantized. The superalgebra of the symmetries present in this model is given. The Noether currents and charges for these symmetries are calculated.     

Canonical quantization of the Skyrme model

The canonical quantization of the Skyrme model is presented. Due to the complexities of the original set-up, first postulated by Rajeev, a new set of fields is found which satisfy a Lie algebra and for this reason, simplifies the study of the system. Using the new fields, the properties of the states under rotations are examined. As a result we re-derive the quantization of the coefficient of the Wess-Zumino action as an a priori consistency condition. We also find under what circumstances states with non-vanishing winding number behave like fermions.     

Canonical quantization

The dynamical variables of a classical system form a Lie algebra , where the Lie multiplication is given by the Poisson bracket. Following the ideas ofSouriau andSegal, but with some modifications, we show that it is possible to realize as a concrete algebra of smooth transformations of the functionals on the manifold of smooth solutions to the classical equations of motion. It is even possible to do this in such a way that the action of a chosen dynamical variable, say the Hamiltonian, is given by the classical motion on the manifold, so that the quantum and classical motions coincide. In this realization, constant functionals are realized by multiples of the identity operator. For a finite number of degrees of freedom,n, the space of functionals can be made into a Hilbert space using the invariant Liouville volume element; the dynamical variablesF become operators in this space. We prove that for any hamiltonianH quadratic in the canonical variablesq ₁...q _n ,p ₁...p _n there exists a subspace ₁ which is invariant under the action of and , and such that the restriction of to ₁ form an irreducible set of operators. Therefore,Souriau's quantization rule agrees with the usual one for quadratic hamiltonians. In fact, it gives the Bargmann-Segal holomorphic function realization. For non-linear problems in general, however, the operators form a reducible set on any subspace of invariant under the action of the Hamiltonian. In particular this happens for . Therefore,Souriau's rule cannot agree with the usual quantization procedure for general non-linear systems.The method can be applied to the quantization of a non-linear wave equation and differs from the usual attempts in that (1) at any fixed time the field and its conjugate momentum may form a reducible set (2) the theory is less singular than usual.For a particular wave equation , we show heuristically that the interacting field may be defined as a first order differential operator acting onc -functions on the manifold of solutions. In order to make this space into a Hilbert space, one must define a suitable method of functional integration on the manifold; this problem is discussed, without, however, arriving at a satisfactory conclusion.On leave from Physics Department, Imperial College, London SW7.Work partly supported by the Office of Scientific Research, U.S. Air Force.     

Canonical quantization with quadratic constraints

Based on an analysis first suggested by Bryce S. DeWitt, we have found that a special case of the general classical theory involving quadratic constraints can be quantized canonically, in the sense that the quantum constraints are consistent. In particular, this special case contains all known physical theories of bosons,including Einstein'sGeneral Theory of Relativity. The quantum constraints for this theory are given explicitly in an appendix.     

A hidden local symmetry approach to rho-meson photoproduction

We study the photoproduction of r \rho -mesons in a model of hidden local symmetry. For this purpose, the r \rho -meson is introduced as a hidden-gauge boson in a non-linear sigma model. For charged r \rho -meson photoproduction, the model takes into account the r \rho -meson magnetic moments from the three-point vertex in the kinetic terms. We show that the magnetic interaction of the charged r \rho -meson has a significant effect on the total cross-sections through the r \rho -meson exchange process, which is proportional to the energy of the photon. The t -channel dominance may be used for the study of structures of various unstable particles.     

Canonical quantization with indefinite inner product

In this paper an algebraic approach to canonical quantization on indefinite inner product space is presented. Concrete realization of such a quantization of a given classical system described by a symplectic space (M, σ) is obtained by means of a so-called J¹-representation of CCR algebra Δ(M, σ). So-called Fock-Krein representations of Δ(M, σ) determined by some class of complex structures on (M, σ) are studied in detail. It is shown that every Fock-Krein representation is unbounded. Starting with a fixed Fock-Krein representation of CCR sectors of non-Fock-Krein representations are constructed.     

Canonical quantization and chromodynamics in a spherical cavity

The canonical quantization formalism is applied to the Lagrange density of chromodynamics, which includes gauge fixing and Faddeev-Popov ghost terms in a general covariant gauge. We develop the quantum theory of the interacting fields in the Dirac picture, based on the Gell-Mann and Low theorem and the Dyson expansion of the time evolution operator. The physical states are characterized by their invariance under Becchi-Rouet-Stora transformations. Subsequently, confinement is introduced phenomenologically by imposing, on the quark, gluon, and ghost field operators, the linear boundary conditions of the MIT bag model at the surface of a spherically symmetric and static cavity. Based on this formalism, we calculate, in the Feynman gauge, all nondivergent Feynman diagrams of second order in the strong coupling constantg. Explicit values of the matrix elements are given for low-lying quark and gluon cavity modes.     

Canonical quantization of gravitation with higher derivatives

A Hamiltonian formalism is constructed for the Lagrangian . This theory is classically quantized. A nontrivial local measure is obtained for the continuum integral, differing from that of Einsteinian gravitation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–9, December, 1985.     

有限空间中Dirac场的正则量子化

研究当存在边界的情形下 Dirac场的正则量子化问题. 采用文献[1]的观点, 将边界条件当作Dirac初级约束.与已有研究不同的是, 本文从离散的角度研究此问题. 将Dirac场的拉氏量和内在约束进行离散化, 并且将离散的边界条件当作初级Dirac约束. 因此, 从约束的起源来看, 这个模型中存在两种不同的约束: 一种是由于模型的奇异性而带来的约束, 即内在约束; 另一种是边界条件. 在对此模型进行正则量子化过程中提出一种能够平等地处理内在约束和边界条件的方法. 为了证明该方法能够平等地对待这两种起源不同的约束, 在计算Dirac 括号时分别选取了两个不同的子集合来构造"中间Dirac括号", 最后得到了相同的结果. 关键词： 边界条件 Dirac约束 Dirac括号     

Canonical quantization of a nonrelativistic singular quasilinear system

Following Dirac's generalized canonical formalism, we develop a quantization scheme for theN-dimensional system described by the Lagrangian which is supposed to be invariant under the gauge transformation . The gauge invariance necessarily implies that the Lagrangian is singular. The identities imposed by the gauge invariance are enumerated and reduced to simpler forms. There are primary and secondary constraints, both of which are of first class. The reduced identities are solved explicitly for the case where the secondary constraints constitute the generators of the groupSO(M), and thus an explicit expression for the manifestly gauge-invariant Lagrangian is obtained. By fixing the gauge appropriately, the unphysical variables are eliminated and a quantization is achieved using only physical variables. Our formulation is covariant under an arbitrary point transformation of physical variables. The problem of formulating a quantum action principle is also commented on briefly.     

Canonical quantization of two-dimensional gravity

A canonical quantization of two-dimensional gravity minimally coupled to real scalar and spinor Majorana fields is presented. The physical state space of the theory is completely described and calculations are also made of the average values of the metric tensor relative to states close to the ground state.