The physical projector and topological quantum field theories:<i>U</i>(1) Chern-Simons theory in 2 + 1 dimensions

Govaerts, Jan; Deschepper, Bernadette

doi:10.1088/0305-4470/33/5/315

Cited by 6 publications

(13 citation statements)

References 25 publications

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“…The nonperturbative solution of the Schwinger model (a U(1) gauge invariant field theory coupled to a massless fermion in 1+1 dimensions) has also been recovered through the physical projector without the necessaity of any gauge fixing. [33] Likewise, the physical projector has been applied [34] to the quantization of the U(1) invariant Chern-Simons theory, one of the simplest topological quantum field theories in which only a finite number of gauge invariant states, dependent only on the differential topology of the spacetime manifold but not its geometry, is to be projected out from an infinite set of quantum states. These successes thus bode well for the relevance of this recent approach towards the quantization of constrained dynamics.…”

Section: Klauder's Physical Projector: Gauge Invariant Quantum Dynamimentioning

confidence: 99%

The Quantum Geometer's Universe: Particles, Interactions and Topology

Govaerts

2002

Contemporary Problems in Mathematical Physics

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With the two most profound conceptual revolutions of XX th century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the three other known fundamental interactions, the physicist of the XXI st century has inherited an unfinished symphony: the unification of the quantum and the continuum. As an invitation to tomorrow's quantum geometers who must design the new rulers by which to size up the Universe at those scales where the smallest meets the largest, these lectures review the basic principles of today's conceptual framework, and highlight by way of simple examples the interplay that presently exists between the quantum world of particle interactions and the classical world of geometry and topology.

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Section: Klauder's Physical Projector: Gauge Invariant Quantum Dynamimentioning

confidence: 99%

The Quantum Geometer's Universe: Particles, Interactions and Topology

Govaerts

2002

Contemporary Problems in Mathematical Physics

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“…When restricted to the physical subspace for which these constraints are satisfied, the above gauge invariant Hamiltonian reduces to a functional depending only on the dynamical physical sector, given by the expression in the first line of (20).…”

Section: The Physical-topological (Pt) Factorisationmentioning

confidence: 99%

“…Our redefinition of fields deals with the original degrees of freedom in such a way that within the Hamiltonian formalism, non propagating (and gauge variant) degrees of freedom are decoupled from the dynamical sector. This latter sector describes only physical degrees of freedom, namely the gauge invariant canonically conjugate electric fields, which diagonalise the physical Hamiltonian (20) in such a way that they acquire a mass through a mixing of the original variables (18). However the Poisson bracket structure remains unaffected since these field redefinitions define merely a canonical transformation.…”

Section: The Physical-topological (Pt) Factorisationmentioning

confidence: 99%

Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

Bertrand

Govaerts

2007

J. Phys. A: Math. Theor.

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Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the 2+1 dimensional Maxwell-Chern-Simons and 3+1 dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However through an appropriate canonical transformation, a gauge invariant factorisation of phase space 1 If p is even with d = 2p, this action reduces to a surface term.

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“…In addition, Klauder [19] has applied the projection operator method in a study of quantum gravity. Finally, a U(1) Chern-Simons model has been studied and solved with the projection operator method using coherent states in [34].…”

Section: Other Applications Of the Pro-jection Operator Approachmentioning

confidence: 99%

Quantization of Constrained Systems

Klauder

2001

Methods of Quantization

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The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first-and second-class constraints from the point of view of coherent-state, phase-space path integration, and show that all such cases may be treated, within the original classical phase space, by using suitable path-integral measures for the Lagrange multipliers which ensure that the quantum system satisfies the appropriate quantum constraint conditions. Unlike conventional methods, our procedures involve no δ-functionals of the classical constraints, no need for dynamical gauge fixing of first-class constraints nor any average thereover, no need to eliminate second-class constraints, no potentially ambiguous determinants, as well as no need to add auxiliary dynamical variables expanding the phase space beyond its original classical formulation, including no ghosts. Besides several pedagogical examples, we also study: (i) the quantization procedure for reparameterization invariant models, (ii) systems for which the original set of Lagrange mutipliers are elevated to the status of dynamical variables and used to define an extended dynamical system which is completed with the addition of suitable conjugates and new sets of constraints and their associated Lagrange multipliers, (iii) special examples of alternative but equivalent formulations of given first-class constraints, as well as (iv) a comparison of both regular and irregular constraints. *

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The physical projector and topological quantum field theories:U(1) Chern-Simons theory in 2 + 1 dimensions

Cited by 6 publications

References 25 publications

The Quantum Geometer's Universe: Particles, Interactions and Topology

The Quantum Geometer's Universe: Particles, Interactions and Topology

Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

Quantization of Constrained Systems

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