Symmetries and ward identities in stochastics quantization

The stochastic quantization of a system with an internal symmetry is discussed in general. It is shown which are the consequences of the symmetry and in particular it is proved that the Ward identities are independent of the quantization scheme.     

Equivalence of Dirac quantization and Schwinger's action principle quantization

We show that the method of Dirac quantization is equivalent to Schwinger's action principle quantization. The relation between the Lagrange undetermined multipliers in Schwinger's method and Dirac's constraint bracket matrix is established and it is explicitly shown that the two methods yield identical (anti)commutators. This is demonstrated in the non-trivial example of supersymmetric quantum mechanics in superspace.     

Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.     

Dirac quantization of open p-brane

We give the scheme of Dirac quantization of open p-brane in the D-brane background. Treating the mixed boundary conditions as primary constraints, we get a set of secondary constraints, then the constraints conditions are shown to be equivalent to orbifold conditions imposed on normal p-brane modes.     

Dirac quantization of a supersymmetric field theory

The superfield of one-space dimensional field theory is quantized using Dirac's method of quantization of systems with constraints. The quantization is shown to be consisted with that of the component fields.     

The quantization of Fermi systems and the Dirac bracket

This work is devoted (a) to discussing some problems related to the quantization rule for constrained classical models of Fermi type, and (b) to working with some detail a specific model which is a classical analogue of the quantum Fermi systems. The quantization of this model is shown to depend on the addition of a total time derivative to the corresponding Lagrangian.     

Quantum field theory of Dirac monopoles and the charge quantization condition

A relativistic quantum field theory of Dirac monopoles in interaction with electric charges is presented. A path-integral quantization is used to discuss the renormalization and derive the Dirac charge quantization condition after higher order effects have been included.     

Anomalous quantization of the free Dirac field in three-dimensional spacetime

The possibility for Bose quantization of the free spinor field in three-dimensional spacetime is demonstrated, compared with Fermi quantization, and discussed.This work is supported in part by the Bulgarian National Foundation for Scientific Research (Ph-20-1991).     

Foundational aspects of geometro-stochastic quantization of Dirac fields in curved spacetime

The application of the recently developed method of geometro-stochastic quantization to spin-1/2 fields in curved spacetime does not give rise to any of the conceptual and technical difficulties encountered by more conventional methods of quantization. Field propagation is based on the concept of stochastic parallel transport governed by quantum connections that incorporate Poincaré gauge invariance and obey the equivalence principle. Consequently, under free-fall conditions, such geometro-stochastic Dirac field propagation does not give rise to Bogolubov transformations resulting in spontaneous fermion creation.1. Supported in part by the NSERC Research Grant No. A5206.2. Supported by an NSERC postgraduate fellowship.     

Dirac propagator from path integral quantization of the pseudoclassical spinning particle

We show how the Dirac propagator can be reproduced by summing over the paths of a pseudoclassical spinning particle.     

Orbital quantization in a system of edge Dirac fermions in nanoperforated graphene

The dependence of the electric resistance R of nanoperforated graphene samples on the position of the Fermi level E _F, which is varied by the gate voltage V _g, has been studied. Nanoperforation has been performed by irradiating graphene samples on a Si/SiO₂ substrate by heavy (xenon) or light (helium) ions. A series of regular peaks have been revealed on the R(V _g) dependence at low temperatures in zero magnetic field. These peaks are attributed to the passage of E _F through an equidistant set of levels formed by orbitally quantized states of edge Dirac fermions rotating around each nanohole. The results are in agreement with the theory of edge states for massless Dirac fermions.     

Secondary quantization of the Dirac free field in hypercomplex system of numbers

The method of secondary quantization of the Dirac free field is developed in the formalism of a hypercomplex system of numbers, generalizing the Clifford algebra to state space analogously to its generalization to distorted space. Then, after conversion to a new basis, it is shown that, taking account of the projection operators, the bases of Fermi algebra — creation and annihilation operators — may be taken as the new basis. Writing the solution of the Dirac free equation in the new basis, the physically observed field values are written in terms of secondary-quantization operators. The adjustable Dirac-field function is calculated in the same formalism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 93–97, October, 1989.     

由正负磁单极对相互作用诱导的孤立狄拉克弦

基于三维旋量Gross-Pitaevskii(GP)方程研究在含时周期性外磁场作用下玻色-爱因斯坦凝聚体的动力学行为.结果显示,在含时周期外磁场的作用下,铁磁态自旋为1的玻色-爱因斯坦凝聚体将发生拓扑形变.当磁场的两个零点进入凝聚体后,自旋向上态的密度布居图在z轴上分别形成向上和向下的凸起.随着磁场的两个零点在凝聚体内...     

Dirac quantization of the supersymmetric nonlinearσ-model on a Riemannian manifold in superspace

We canonically quantize the supersymmetric nonlinear σ-model on a Riemannian manifold using the superfield language. The resulting quantization is consistent with those of the component fields.     

The positronium negative ion: Classical properties aaand semiclassical quantization

Properties of collinear and planar periodic orbits for the positronium negative ion are examined with respect to the possibilities for semiclassical quantization. In contrast to other two-electron atomic systems as helium and H^- the relevant orbits for quantization are fully stable and permit a full torus quantization. However, for lower excitations the area of stability in phase-space is too small for a reliable torus quantization. Instead, a quasi-separability of the three-body system is used to apply effective one-dimensional (WKB) quantization. Received 19 January 2001     

Mass and dual mass: A gravitational analogue of the Dirac quantization rule and its physical implications

It is shown that (asymptotically multi-NUT) gravitational magnetic monopoles, which can be described by anS ³/Z _N principal Hopf-bundle structure at conformal null infinity (Z _N is a cyclic subgroup of orderN ofZ). provide a gravitational analogue of the Dirac quantization rule, which involves the total magnetic (dual) mass of the space-time-a measurement of the first Chern class of the bundle-and the mass of a test particle located in the rest frame defined at infinity by the Bondi (or dual Bondi) 4-momentum. It is shown thatSU ₂/U ₁ preserves the asymptotic structure. A definition of the angular momentum operator which extends that available for test electric charges in the field of a (Maxwellian) Yang-Wu magnetic monopole is presented. The commutation relations are dictated by the quantization rule. Various physical consequences are mentioned. SinceSU ₂ is a double covering ofSO ₃, gravitational magnetic monopoles provide a topological explanation for the existence of particles with half-integer spin. Abelian (U ₁), non-AbelianSU ₁ asymptotic degrees of freedom of the gravitational field could be related to suitable nontrivial cohomology classes; Penrose's nonlinear graviton modes could emerge as self (antiself) adjoint (Yang-Mills) gauge connections.     

Recursive properties of Dirac and metriplectic Dirac brackets with applications

In this article, we prove that Dirac brackets for Hamiltonian and non-Hamiltonian constrained systems can be derived recursively. We then study the applicability of that formulation in analysis of some interesting physical models. Particular attention is paid to the feasibility of implementation code for Dirac brackets in Computer Algebra System.