5,357 research outputs found
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.
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
The Electromagnetic and Proca Fields Revisited: a Unified Quantization
Quantizing the electromagnetic field with a group formalism faces the
difficulty of how to turn the traditional gauge transformation of the vector
potential, , 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, , acquire dynamical content outside the
photon mass shell, a fact which also allows a unified quantization of both the
electromagnetic and Proca fields.Comment: 16 pages, latex, no figure
Group Quantization on Configuration Space: Gauge Symmetries and Linear Fields
A new, configuration-space picture of a formalism of group quantization, the
GAQ formalism, is presented in the context of a previous, algebraic
generalization. This presentation serves to make a comprehensive discussion in
which other extensions of the formalism, particularly to incorporate gauge
symmetries, are developed as well. Both images are combined in order to
analyse, in a systematic manner and with complete generality, the case of
linear fields (abelian current groups). To ilustrate these developments we
particularize them for several fields and, in particular, we carry out the
quantization of the abelian Chern-Simons models over an arbitrary closed
surface in detail.Comment: Plain LaTeX, 31 pages, no macros. To appear in J. Math. Phy
Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory
The underlying reasons for the difficulty of unitarily implementing the whole
conformal group in a massless Quantum Field Theory (QFT) are
investigated in this paper. Firstly, we demonstrate that the singular action of
the subgroup of special conformal transformations (SCT), on the standard
Minkowski space , cannot be primarily associated with the vacuum radiation
problems, the reason being more profound and related to the dynamical breakdown
of part of the conformal symmetry (the SCT subgroup, to be more precise) when
representations of null mass are selected inside the representations of the
whole conformal group. Then we show how the vacuum of the massless QFT radiates
under the action of SCT (usually interpreted as transitions to a uniformly
accelerated frame) and we calculate exactly the spectrum of the outgoing
particles, which proves to be a generalization of the Planckian one, this
recovered as a given limit.Comment: 29 pages, Latex, 1 figure, to appear in Commun. Math. Phy
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
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
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
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