0000000000061447
AUTHOR
Victor Aldaya
showing 12 related works from this author
Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
1988
We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the ‘renormalization’ β factor of L(z)
Quantization on the Virasoro group
1990
The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…
Higher-Order Differential Operators on a Lie Group and Quantization
1995
This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or representations of Lie groups in those anomalous cases where the Kostant-Kirilov co-adjoint method or the Borel-Weyl-Bott representation algorithm do not succeed.
Generalized Conformal Symmetry and Extended Objects from the Free Particle
1998
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphi…
The quantum relativistic harmonic oscillator: generalized Hermite polynomials
1991
A relativistic generalisation of the algebra of quantum operators for the harmonic oscillator is proposed. The wave functions are worked out explicitly in configuration space. Both the operator algebra and the wave functions have the appropriate c→∞ limit. This quantum dynamics involves an extra quantization condition mc2/ωℏ = 1, 32, 2, … of a topological character.
Covariant phase-space quantization of the induced 2D gravity
1993
Abstract We study in a parallel way the induced 2D gravity and the Jackiw-Teitelboimmodel on the cylinder from the viewpoint of the covariant description of canonical formalism. We compute explicity thhe symplectic structure of both theories showing that their (reduced) phase spaces are finite-dimensional cotangent bundles. For the Jackiw-Teitelboim model the base space (configuration space) is the space of conjugacy classes of the PSL(2, R ) group. For the induced 2D gravity, and Λ > 0, the (reduced) phase space consist of two (identical) connected components each one isomorphic to the contangent bundle of the space of hyperbolic conjugacy classes of the PSL (2, R ) group, whereas for Λ R …
Covariant phase space quantization of the Jackiw-Teitelboim model of two-dimensional gravity
1992
Abstract On the basis of the covariant phase space formulation of field theory we analyze the Jackiw-Teitelboim model of two-dimensional gravity on a cylinder. We compute explicitly the symplectic structure showing that the (reduced) phase space is the cotangent bundle of the space of conjugacy classes of the PSL(2, R ) group. This makes it possible to quantize the theory exactly. The Hilbert space is given by the character functions of the PSL (2, R ) group. As a byproduct, this implies the complete equivalence with the PSL (2, R )-topological gravity model.
New solutions of the hamiltonian and diffeomorphism constraints of quantum gravity from a highest weight loop representation
1991
Abstract We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space.
The electromagnetic and Proca fields revisited: A unified quantization
1997
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…
Formal Group Laws for Affine Kac-Moody groups and group quantization
1987
We describe a method for obtaining Formal Group Laws from the structure constants of Affine Kac-Moody groups and then apply a group manifold quantization procedure which permits construction of physical representations by using only canonical structures on the group. As an intermediate step we get an explicit expression for two-cocycles on Loop Groups. The programme is applied to the AffineSU(2) group.
Higher-order polarizations on the Virasoro group and anomalies
1991
In a previous paper the authors showed that the space of (first order) polarized functions on the Virasoro group is not, in general, irreducible. The full reduction was explicitly achieved by taking the orbit of the enveloping algebra through the vacuum. This additional step provided the proper quantization in the “strong-coupling” domain 0<c≦1. In this paper we introduce the concept of “higher order polarization” as a generalization of that of polarization. We prove that the imposing of the additional (higher-order) polarization conditions is equivalent to the taking of the above-mentioned orbit. This demonstrates that the generalized (higher-order) polarization conditions suffice to obtai…
Algebraic quantization on a group and nonabelian constraints
1989
A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central)U(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.