Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting Q_BRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincaré symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.     

Covariant canonical quantization of fields and Bohmian mechanics

We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard non-covariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional non-covariant Wheeler-DeWitt approach.Received: 11 October 2004, Published online: 6 July 2005PACS: 04.20.Fy, 04.60.Ds, 04.60.Gw, 04.60.-m     

Covariant canonical formalism for gravity

We continue the previous discussion (A. D'Adda, J. E. Nelson, and T. Regge, Ann. Phys. (N.Y.)165) of the covariant canonical formalism for the group manifold and relate it to the standard canonical vierbein formalism as pioneered by Dirac. The form bracket is related to the Poisson bracket of classical mechanics. We utilise systematically the calculus of differential forms and a compound notation which labels Poincaré multiplets. In this way we obtain a particularly clear and compact expression for the Hamiltonian and the constraints algebra of the vierbein formalism.     

Hopfion canonical quantization

We study the effect of the canonical quantization of the rotational mode of the charge Q=1$Q=1$ and Q=2$Q=2$ spinning Hopfions. The axially-symmetric solutions are constructed numerically, it is shown the quantum corrections to the mass of the configurations are relatively large.     

Covariant quantization of chiral bosons and anomaly cancellation

A bosonic string with D spacetime dimensions, R right-moving internal scalars and L left-moving ones can be quantized canonically and is free from local anomaliesif R=L=26−D. Actions for such string theories can be written using Siegel's action for chiral bosons, but anomaly cancellation requires D=0, R=L=26. An action is presented that describes chiral string theories provided R=L=26−D and the physical spectrum is shown to be identical to that of the canonically constructed theory. Supersymmetry, curved backgrounds and global anomalies are briefly discussed.     

Covariant quantization of non-Abelian antisymmetric tensor gauge theories

The non-Abelian Freedman-Townsend gauge tensor model is quantized in large class of covariant gauges using the geometrical reinterpretation of the BRS equations. In addition to the now usual pyramid of gauge and ghost states, a pyramid of auxiliary fields is found in our construction. These fields enforce the consistency of equations of motion and the integrability of the BRS equations.     

Covariant quantization of string based on BRS invariance

Covariant canonical quantization of the bosonic string is performed, based on the BRS invariance principle. Defining a physical state by a modified form of Kugo-Ojima's subsidiary condition Q_B|phys〉 = 0 (Q_B = BRS charge), we prove a no-ghost theorem in a simple manner. There an interesting relation between critical dimension and BRS symmetry is noticed; namely, the conditions D = 26 and α₀ = 1 for the space-time dimension D and the zero-intercept α₀ of leading trajectory are required by the nilpotency Q_B² = 0 of the BRS charge. In addition, ghost number fractionization is observed in this system.     

Covariant Mellin transforms and the Weyl group quantization

The outline of the formalism with diagonalized dilation generator is presented. The covariant Mellin transform defining quanta with definite dimensionality and SL(2, C) quantum numbers is proposed.     

Covariant quantization of gauge fields without Gribov ambiguity

Recently Parisi and Wu proposed a method of quantizing gauge fields whereby euclidean expectation values are obtained by relaxation to equilibrium of a stochastic process depending on an artificial fifth time parameter. In the present work the equilibrium distribution is determined directly, without reference to the artificial time, by a stationary condition which is an eigenfunction equation in the euclidean Hilbert space. The solution has a perturbative expansion which appears renormalizable by naive power counting. Because of gauge freedom, a free dimensionless gauge parameter appears in the theory although no gauge condition such as ? · A = 0 is imposed.     

Baby Skyrmions stabilized by canonical quantization

We analyse the effect of the canonical quantization of the rotational mode of the O(3)$O(3)$σ  -model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge n=1,2$n=1,2$ configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.     

Generalized canonical osp(1,2) quantization

A possibility of constructing a generalized canonical quantization for arbitrary dynamical systems with first-class constrains is considered based on the invariance principle of the osp(1,2) global supersymmetry. Tomsk State Pedagogical University, Russia; Departamento de Fisica, ICE, Universidade Federal de Juize de Fora, Brazil. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–6, October, 1999.     

Nonstandard canonical quantization of local field theories

A recent new approach to classical local field theories (CLFT) offers a new, alternative quantization procedure of fields. A brief discussion of this nonstandard field quantization is given.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Equivalence of stochastic and canonical quantization in perturbation theory

It is shown that the stochastic quantization method introduced by Parisi and Wu reproduces, order by order, the ordinary perturbation expansion. The proof is valid for any field theory, including gauge theories, provided one considers gauge-invariant quantities.