Quantum Physics and Fluctuating Topologies: Survey

Asorey, M.; Balachandran, A. P.; Marmo, Giuseppe; Silva, I. P. Costa e; Queiroz, Amilcar R. de; Teotonio-Sobrinho, P.; Vaidya, Sachindeo

doi:10.48550/arxiv.1211.6882

Cited by 9 publications

(12 citation statements)

References 25 publications

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“…Most of the boundary conditions are non-local and some of them can be experimentally implemented coating the boundary with suitable metamaterials. Some of them involve topology changes [31,29] which motivated recent interesting proposals related to quantum gravity [32,33]. The vacuum state of the scalar free field theory with boundary condition U ∈ M F is unique and given by…”

Section: Vacuum Energy Of Bosonic Massless Fields In Bounded Domainsmentioning

confidence: 99%

Attractive and repulsive Casimir vacuum energy with general boundary conditions

2013

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The infrared behavior of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth-Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.

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Section: Vacuum Energy Of Bosonic Massless Fields In Bounded Domainsmentioning

confidence: 99%

Attractive and repulsive Casimir vacuum energy with general boundary conditions

2013

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“…, s ∈ [0, 1] of unitary matrices of U (4), interpolating between the matrices U 2 and U 1 . In this way a topology fluctuation phenomena can be described in very a simple manner in terms of boundary conditions [1,5,6]. The absolute principle of strict conservation of the quantum probability in a bounded domain Ω ⊂ R is not realistic, because most of the physical boundaries are Fig.…”

Section: Boundary Effects In Quantum Mechanicsmentioning

confidence: 99%

“…The space of boundary conditions compatible with both constraints has interesting global geometric properties. The dependence of many interesting physical phenomena, like the Casimir effect [3], topology change [4,1,5,6] or renormalization group flows [7], on the boundary conditions can be analyzed from this global perspective.…”

Section: Introductionmentioning

confidence: 99%

Boundary effects in bosonic and fermionic field theories

Asorey

García-Álvarez

Munõz-Castañeda

2015

Int. J. Geom. Methods Mod. Phys.

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The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle for scalar and fermionic quantum field theories. Unitarity arises as a consequence of the choice of charge preserving boundary conditions. This provides a powerful framework for the analysis of global geometrical and topological properties of the space of physical boundary conditions. Boundary conditions which allow the existence of edge states can only arise in theories with a mass gap which is also a physical requirement for topological insulators.

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“…According to the postulates of quantum mechanics, a quadratic form corresponds to a physical observable-and hence to a self-adjoint operator-if and only if it is real and closed [28]. Therefore, the search of the self-adjoint extensions of the symmetric operator T is mirrored in the search of the real and closed quadratic forms that extend the minimal form (2).…”

Section: Quadratic Formsmentioning

confidence: 99%

Self-adjoint extensions and unitary operators on the boundary

2017

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Abstract. We establish a bijection between the self-adjoint extensions of the Laplace operator on a bounded regular domain and the unitary operators on the boundary. Each unitary encodes a specific relation between the boundary value of the function and its normal derivative. This bijection sets up a characterization of all physically admissible dynamics of a nonrelativistic quantum particle confined in a cavity. Moreover, this correspondence is discussed also at the level of quadratic forms. Finally, the connection between this parametrization of the extensions and the classical one, in terms of boundary self-adjoint operators on closed subspaces, is shown.

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Quantum Physics and Fluctuating Topologies: Survey

Cited by 9 publications

References 25 publications

Attractive and repulsive Casimir vacuum energy with general boundary conditions

Attractive and repulsive Casimir vacuum energy with general boundary conditions

Boundary effects in bosonic and fermionic field theories

Self-adjoint extensions and unitary operators on the boundary

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