Group Approach to Quantization of Yang-Mills Theories: A Cohomological Origin of Mass

New clues for the best understanding of the nature of the symmetry-breaking mechanism are revealed in this paper. A revision of the standard gauge transformation properties of Yang-Mills fields, according to a group approach to quantization scheme, enables the gauge group coordinates to acquire dynamical content outside the null mass shell. The corresponding extra (internal) field degrees of freedom are transferred to the vector potentials to conform massive vector bosons.Comment: 21 pages, LaTeX, no figures; final for

Dynamical content of quantum diffeomorphisms in two-dimensional quantum gravity

A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central extension for the critical values of the conformal anomaly. The rest of the generators in the group, L_n (n>1, n<-1), mix space-times with different constant curvature. Only in the classical limit all space-times can be identified, defining a unique Minkowski space-time, and the operators L_n (n<1, n<-1) gauged away. This process entails a restriction to SL(2,R) subrepresentations, which creates a non-trivial two-dimensional symplectic classical phase space. The present model thus suggests that the role of general covariance in quantum gravity is different from that played in the classical limit.Comment: 4 pages, LaTeX, no figures; uses espcrc2.sty (twocolumn). Contribution to the "Third Meeting on Constrained Dynamics and Quantum Gravity QG99" held in Sardinia, Italy, on Sept. 1999. To appear in Nucl. Phys. B (Proc. Suppl.

Finite-Difference Equations in Relativistic Quantum Mechanics

Relativistic Quantum Mechanics suffers from structural problems which are traced back to the lack of a position operator $\hat{x}$, satisfying $[\hat{x},\hat{p}]=i\hbar\hat{1}$ with the ordinary momentum operator $\hat{p}$, in the basic symmetry group -- the Poincar\'e group. In this paper we provide a finite-dimensional extension of the Poincar\'e group containing only one more (in 1+1D) generator $\hat{\pi}$, satisfying the commutation relation $[\hat{k},\hat{\pi}]=i\hbar\hat{1}$ with the ordinary boost generator $\hat{k}$. The unitary irreducible representations are calculated and the carrier space proves to be the set of Shapiro's wave functions. The generalized equations of motion constitute a simple example of exactly solvable finite-difference set of equations associated with infinite-order polarization equations.Comment: 10 LaTeX pages, final version, enlarged (2 more pages

Space-time dynamics from algebra representations

We present a model for introducing dynamics into a space-time geometry. This space-time structure is constructed from a C*-algebra defined in terms of the generators of an irreducible unitary representation of a finite-dimensional Lie algebra G. This algebra is included as a subalgebra in a bigger algebra F, the generators of which mix the representations of G in a way that relates different space-times and creates the dynamics. This construction can be considered eventually as a model for 2-D quantum gravity.Comment: 6 pages, LaTeX, no figures. Old paper submitted for archive reason

New insights in particle dynamics from group cohomology

The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincare or Galilei) by making local some subgroup. The corresponding dynamics is generated by a vector field inside the kernel of a presymplectic form which is derived from the canonical left-invariant one-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inonu-Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a non-trivial mixing of gravity and electromagnetism leading to in principle testable predictions.Comment: 8 pages, LaTeX, no figures. To appear in J. Phys. A (Letter to the editor

Algebraic characterization of constraints and generation of mass in gauge theories

The possibility of non-trivial representations of the gauge group on wavefunctionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters "m" show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons.Comment: 4 pages, LaTeX, no figures; uses espcrc2.sty (twocolumn). Contribution to the "Third Meeting on Constrained Dynamics and Quantum Gravity QG99" held in Sardinia, Italy, on Sept. 1999. To appear in Nucl. Phys. B (Proc. Suppl.

Space-time Structures from Critical Values in 2D Quantum Gravity

A model for 2D Quantum Gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,R) generators) lose their dynamical content (they are no longer conjugated operators). The notion of space-time itself in 2D gravity then arises as associated with this kinematical SL(2,R) symmetry. An ensemble of different copies of AdS do co-exist in this model with different weights, depending on their curvature (which is proportional to \hbar^{2}) and they are connected by gravity operators. This model suggests that, in general, quantum diffemorphisms should not be imposed as constraints to the theory, except for the classical limit.Comment: 22 pages, latex, no figures. Revised version with an effort in the development of the underlying classical theory and the clarification of the classical limit. To appear in Class. Quant. Gra

Coupling Nonlinear Sigma-Matter to Yang-Mills Fields: Symmetry Breaking Patterns

We extend the traditional formulation of Gauge Field Theory by incorporating the (non-Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinear-sigma-model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling prescription, which resembles the so-called Stueckelberg transformation, but for the non-Abelian case. Here we study the case of internal gauge symmetry groups, in particular, unitary groups U(N). We show how to couple standard Yang-Mills Theory to Nonlinear-Sigma Models on cosets of U(N): complex projective, Grassman and flag manifolds. These different couplings lead to distinct (chiral) symmetry breaking patterns and \emph{Higgs-less} mass-generating mechanisms for Yang-Mills fields.Comment: 11 pages. To appear in Journal of Nonlinear Mathematical Physic

Group-quantization of non-linear sigma models: particle on S^2 revisited

We present the quantum mechanics of "partial-trace" non-linear sigma models, on the grounds of a fully symmetry-based procedure. After the general scheme is sketched, the particular example of a particle on the two-sphere is explicitly developed. As a remarkable feature, no explicit constraint treatment is required nor ordering ambiguities do appear. Moreover, the energy spectrum is recovered without extra terms in the curvature of the sphere.Comment: 8 page