On the relation between rigging inner product and master constraint direct integral decomposition

@article{Han2010OnTR,
  title={On the relation between rigging inner product and master constraint direct integral decomposition},
  author={Muxin Han and Thomas Thiemann},
  journal={Journal of Mathematical Physics},
  year={2010},
  volume={51},
  pages={092501-092501}
}
Canonical quantization of constrained systems with first-class constraints via Dirac’s operator constraint method proceeds by the theory of Rigged Hilbert spaces, sometimes also called refined algebraic quantization. This method can work when the constraints form a Lie algebra. When the constraints only close with nontrivial structure functions, the Rigging map can no longer be defined. To overcome this obstacle, the master constraint method has been proposed which replaces the individual… 
On the relation between operator constraint, master constraint, reduced phase space and path integral quantization
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space
Rescaling Constraints, BRST Methods, and Refined Algebraic Quantisation
We investigate the canonical BRST–quantisation and refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling
Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
Spin Foam Models are supposed to be discretised path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration
Relation Between Regge Calculus and BF Theory on Manifolds with Defects
In Regge calculus, the space–time manifold is approximated by certain abstract simplicial complex, called a pseudomanifold, and the metric is approximated by an assignment of a length to each
A path integral for the master constraint of loop quantum gravity
In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint program. The physical inner product is expressed by using the group averaging technique for
M ay 2 01 2 The new spin foam models and quantum gravity
The quantization of the gravitational interaction is a major open challenge in theoretical physics. This review presents the status of the spin foam approach to the problem. Spin foam models are
2+1 gravity with positive cosmological constant in LQG: a proposal for the physical state
In this paper, I investigate the possible quantization, in the context of loop quantum gravity, of three-dimensional gravity in the case of positive cosmological constant Λ and try to make contact
$\operatorname{SL}(2,\mathbb{C})$ Chern-Simons theory, flat connections, and four-dimensional quantum geometry
The present paper analyze SL(2,C) Chern-Simons theory on a class of graph complement 3- manifolds, and its relation with classical and quantum geometries on 4-dimensional manifolds. In classical
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude on a 4D simplicial complex with arbitrary number of simplices. We show that for a critical configuration {jf, gve, nef}
...
1
2
3
...

References

SHOWING 1-10 OF 60 REFERENCES
On the relation between operator constraint, master constraint, reduced phase space and path integral quantization
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space
Quantum spin dynamics: VIII. The master constraint
Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is
The Holst Spin Foam Model via Cubulations
Spin foam models are an attempt for a covariant, or path integral formulation of canonical loop quantum gravity. The construction of such models usually rely on the Plebanski formulation of general
Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product
This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from
A Uniqueness theorem for constraint quantization
This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called `rigging maps' associated with refined algebraic
Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models
This is the third paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. In this work, we analyse models which,
On the generality of refined algebraic quantization
The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular
Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
TLDR
It is shown that the master constraint programme has a wide range of applicability but that there are many, physically interesting subtleties that must be taken care of in doing so.
Canonical path integral measures for Holst and Plebanski gravity: I. Reduced phase space derivation
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is
Testing the master constraint programme for loop quantum gravity : V. Interacting field theories
This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting
...
1
2
3
4
5
...