843 research outputs found

### Fundamentals of Quantum Gravity

The outline of a recent approach to quantum gravity is presented. Novel
ingredients include: (1) Affine kinematical variables; (2) Affine coherent
states; (3) Projection operator approach toward quantum constraints; (4)
Continuous-time regularized functional integral representation without/with
constraints; and (5) Hard core picture of nonrenormalizability. The ``diagonal
representation'' for operator representations, introduced by Sudarshan into
quantum optics, arises naturally within this program.Comment: 15 pages, conference proceeding

### The Affine Quantum Gravity Program

The central principle of affine quantum gravity is securing and maintaining
the strict positivity of the matrix \{\hg_{ab}(x)\} composed of the spatial
components of the local metric operator. On spectral grounds, canonical
commutation relations are incompatible with this principle, and they must be
replaced by noncanonical, affine commutation relations. Due to the partial
second-class nature of the quantum gravitational constraints, it is
advantageous to use the recently developed projection operator method, which
treats all quantum constraints on an equal footing. Using this method,
enforcement of regularized versions of the gravitational operator constraints
is formulated quite naturally by means of a novel and relatively well-defined
functional integral involving only the same set of variables that appears in
the usual classical formulation. It is anticipated that skills and insight to
study this formulation can be developed by studying special, reduced-variable
models that still retain some basic characteristics of gravity, specifically a
partial second-class constraint operator structure. Although perturbatively
nonrenormalizable, gravity may possibly be understood nonperturbatively from a
hard-core perspective that has proved valuable for specialized models. Finally,
developing a procedure to pass to the genuine physical Hilbert space involves
several interconnected steps that require careful coordination.Comment: 16 pages, LaTeX, no figure

### On the role of coherent states in quantum foundations

Coherent states, and the Hilbert space representations they generate, provide
ideal tools to discuss classical/quantum relationships. In this paper we
analyze three separate classical/quantum problems using coherent states, and
show that useful connections arise among them. The topics discussed are: (1) a
truly natural formulation of phase space path integrals; (2) how this analysis
implies that the usual classical formalism is ``simply a subset'' of the
quantum formalism, and thus demonstrates a universal coexistence of both the
classical and quantum formalisms; and (3) how these two insights lead to a
complete analytic solution of a formerly insoluble family of nonlinear quantum
field theory models.Comment: ICQOQI'2010, Kiev, Ukraine, May-June 2010, Conference Proceedings (9
pages

### The Utility of Coherent States and other Mathematical Methods in the Foundations of Affine Quantum Gravity

Affine quantum gravity involves (i) affine commutation relations to ensure
metric positivity, (ii) a regularized projection operator procedure to
accomodate first- and second-class quantum constraints, and (iii) a hard-core
interpretation of nonlinear interactions to understand and potentially overcome
nonrenormalizability. In this program, some of the less traditional
mathematical methods employed are (i) coherent state representations, (ii)
reproducing kernel Hilbert spaces, and (iii) functional integral
representations involving a continuous-time regularization. Of special
importance is the profoundly different integration measure used for the
Lagrange multiplier (shift and lapse) functions. These various concepts are
first introduced on elementary systems to help motivate their application to
affine quantum gravity.Comment: 15 pages, Presented at the X-International Conference on Symmetry
Methods in Physic

### Divergence-free Nonrenormalizable Models

A natural procedure is introduced to replace the traditional, perturbatively
generated counter terms to yield a formulation of covariant, self-interacting,
nonrenormalizable scalar quantum field theories that has the added virtue of
exhibiting a divergence-free perturbation analysis. To achieve this desirable
goal it is necessary to reexamine the meaning of the free theory about which
such a perturbation takes place.Comment: 22 pages. Version accepted for publication; involves modest addition
to the end of Sec.

### Enhanced quantization on the circle

We apply the quantization scheme introduced in [arXiv:1204.2870] to a
particle on a circle. We find that the quantum action functional restricted to
appropriate coherent states can be expressed as the classical action plus
$\hbar$-corrections. This result extends the examples presented in the cited
paper.Comment: 7 page

### Ultralocal Fields and their Relevance for Reparametrization Invariant Quantum Field Theory

Reparametrization invariant theories have a vanishing Hamiltonian and enforce
their dynamics through a constraint. We specifically choose the Dirac procedure
of quantization before the introduction of constraints. Consequently, for field
theories, and prior to the introduction of any constraints, it is argued that
the original field operator representation should be ultralocal in order to
remain totally unbiased toward those field correlations that will be imposed by
the constraints. It is shown that relativistic free and interacting theories
can be completely recovered starting from ultralocal representations followed
by a careful enforcement of the appropriate constraints. In so doing all
unnecessary features of the original ultralocal representation disappear.
The present discussion is germane to a recent theory of affine quantum
gravity in which ultralocal field representations have been invoked before the
imposition of constraints.Comment: 17 pages, LaTeX, no figure

### Linearized Quantum Gravity Using the Projection Operator Formalism

The theory of canonical linearized gravity is quantized using the Projection
Operator formalism, in which no gauge or coordinate choices are made. The ADM
Hamiltonian is used and the canonical variables and constraints are expanded
around a flat background. As a result of the coordinate independence and linear
truncation of the perturbation series, the constraint algebra surprisingly
becomes partially second-class in both the classical and quantum pictures after
all secondary constraints are considered. While new features emerge in the
constraint structure, the end result is the same as previously reported: the
(separable) physical Hilbert space still only depends on the
transverse-traceless degrees of freedom.Comment: 30 pages, no figures, enlarged and corrected versio

### Ladder operators and coherent states for continuous spectra

The notion of ladder operators is introduced for systems with continuous
spectra. We identify two different kinds of annihilation operators allowing the
definition of coherent states as modified "eigenvectors" of these operators.
Axioms of Gazeau-Klauder are maintained throughout the construction.Comment: Typos correcte

### Generalized Affine Coherent States: A Natural Framework for Quantization of Metric-like Variables

Affine variables, which have the virtue of preserving the positive-definite
character of matrix-like objects, have been suggested as replacements for the
canonical variables of standard quantization schemes, especially in the context
of quantum gravity. We develop the kinematics of such variables, discussing
suitable coherent states, their associated resolution of unity, polarizations,
and finally the realization of the coherent-state overlap function in terms of
suitable path-integral formulations.Comment: 17 pages, LaTeX, no figure

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