Semiclassical Expansions, the Strong Quantum Limit, and Duality

Isidro, J. M.

doi:10.1142/s0217732305019055

Cited by 4 publications

(6 citation statements)

References 7 publications

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“…On the other hand, we have in ref. [6] shown that the existence of a minimal length scale L P is equivalent to the exchange…”

Section: Introductionmentioning

confidence: 99%

Quantum Mechanics as a Spontaneously Broken Gauge Theory on a U(1) Gerbe

Isidro

2008

Int. J. Geom. Methods Mod. Phys.

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Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/ ), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a point-by-point basis on configuration space. This is equivalent to the statement that quantum mechanics is a U(1) gauge theory. Unlike Yang-Mills theories, however, the geometry of this gauge symmetry is not given by a fibre bundle, but rather by a gerbe. Since this gauge symmetry is spontaneously broken, an analogue of the Higgs mechanism must be present. We prove that a Heisenberg-like noncommutativity for the space coordinates is responsible for the breaking. This allows to interpret the noncommutativity of space coordinates as a Higgs mechanism on the quantum-mechanical U(1) gerbe.

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“…On the other hand, we have in ref. [6] shown that the existence of a minimal length scale L P is equivalent to the exchange…”

Section: Introductionmentioning

confidence: 99%

Quantum Mechanics as a Spontaneously Broken Gauge Theory on a U(1) Gerbe

Isidro

2008

Int. J. Geom. Methods Mod. Phys.

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“…In this letter we have established the equivalence between the duality (2) and that proposed in ref. [5], which can be summarised in eqn. (4).…”

Section: Discussionmentioning

confidence: 99%

“…As stressed in ref. [5], the auxiliary particle of mass m is not to be confused with the physical degrees of freedom of the action S under consideration in eqn. (3).…”

Section: Equivalence Of Dualitiesmentioning

confidence: 99%

A QUANTUM-GRAVITY PERSPECTIVE ON SEMICLASSICAL vs. STRONG-QUANTUM DUALITY

Isidro

2006

Int. J. Geom. Methods Mod. Phys.

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It has been argued that, underlying M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this letter we prove that the above semiclassical vs. strongquantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.

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“…[5] is equivalent to a Heisenberg-algebra noncommutativity [6] for the space coordinates. The connection on the gerbe is interpreted physically as a Neveu-Schwarz field B µν or, equivalently, as the magnetic background [7] that causes space coordinates to stop being commutative and close a Heisenberg algebra instead.…”

Section: Introductionmentioning

confidence: 99%

“…is closely related to the trivialisation of a gerbe on F. This fact can be used in order to prove that the semiclassical vs. strong-quantum duality S/ ↔ /S of ref. [5] is equivalent to a Heisenberg-algebra noncommutativity [6] for the space coordinates.…”

Section: Introductionmentioning

confidence: 99%