5,130 research outputs found
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 , satisfying
with the ordinary momentum operator
, 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 , satisfying the commutation
relation with the ordinary boost generator
. 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
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