Loop-space quantum formulation of free electromagnetism

Bartolo, Cayetano Di; Nori, Franco; Gambini, Rodolfo; Trías, A.

doi:10.1007/bf02787033

Cited by 53 publications

(50 citation statements)

References 10 publications

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“…Here γ • γ ′ denotes the Abelian group of loops product [14,15]. It is worth recalling that an Abelian loop is an equivalence class of closed curves, defined as follows.…”

Section: Maxwell Theorymentioning

confidence: 99%

Geometric approach to a massivepform duality

2003

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Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2 + 1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.

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“…Here γ • γ ′ denotes the Abelian group of loops product [14,15]. It is worth recalling that an Abelian loop is an equivalence class of closed curves, defined as follows.…”

Section: Maxwell Theorymentioning

confidence: 99%

Geometric approach to a massivepform duality

2003

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“…The path representation arises when one considers path dependent wave functionals Ψ[γ], and realizes the canonical field operators by means of operations onto these wave functionals [3][4][5]14]. We define the path and loop derivatives δ i ( x) and ∆ ij ( x) by…”

Section: Quantization and Loop Representationmentioning

confidence: 99%

“…Often, it happens that different approaches to understand the formulation of Dirac bring out novelties or unexpected relationships between old things. Being a gauge theory, the Dirac theory of magnetic poles should be a candidate to admit a quantum geometric representation, such as the Loop Representation (LR) of Maxwell theory [3][4][5]. In this article we address this point to some extent.…”

Section: Introductionmentioning

confidence: 99%

Magnetic monopole in the loop representation

Leal

López

2006

Journal of Mathematical Physics

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We quantize, within the Loop Representation formalism, the electromagnetic field in the presence of a static magnetic pole. It is found that loop-dependent physical wave functionals acquire a topological dependence on the surfaces bounded by the loop. This fact generalizes what occurs in ordinary quantum mechanics in multiply connected spaces. When Dirac's quantization condition is satisfied, the dependence on the surfaces disappears, together with the influence of the monopole on the quantized electromagnetic field.

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“…In the case of quantum gravity the loop wavefunctions are knot invariants and their analytic expressions require the introduction of a regularization (framing). This difficulty not only arises for the gravitational case, even in the simple case of a free Maxwell field [24], it is known that the quantum states in the loop representation are ill defined and a regularization is needed. In the extended representation the second difficulty can be solved.…”

Section: The Issue Of the Regularizationmentioning

confidence: 99%

Extended loop representation of quantum gravity

Bartolo

Gambini²,

Griego³

1995

Phys. Rev. D

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A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum Gravity can be realized on the state space of extended loop dependent wavefunctions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and hamiltonian constraints take a very simple form and allow to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. The practical calculation advantages allows to find a new solution to the Wheeler-DeWitt equation. Moreover, the extended representation puts in a precise framework some of the regularization problems of the loop representation. We show that the solutions are generalized knot invariants, smooth in the extended variables, and any framing is unnecessary.

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Loop-space quantum formulation of free electromagnetism

Cited by 53 publications

References 10 publications

Geometric approach to a massivepform duality

Geometric approach to a massivepform duality

Magnetic monopole in the loop representation

Extended loop representation of quantum gravity

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