Mechanical similarity as a generalization of scale symmetry

A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton-Hooke symmetry are constructed. *

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“…Such transformations cannot be promoted to symmetries at the quantum level, see Ref. [24] for the discussion.…”

Section: Classical Dynamicsmentioning

confidence: 99%

(2+1)D exotic Newton–Hooke symmetry, duality and projective phase

et al. 2007

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“…This single bound state is however a characteristic feature of the of the inverse square potential and has been obtained in literature [4,5,7,14,24,25,26,27,28,29,30] before. Note that the motion along z direction is still given by a free particle solution e ikz .…”

Section: Scaling Anomaly Of Na Systemmentioning

confidence: 86%

“…We now discuss scaling symmetry and its anomaly [24,25,26,27,28,29] for the full 3-dimensional problem of a neutral atom in the magnetic field of a ferromagnetic wire. Classically the action constructed from the Hamiltonian H = p 2 /2µ − µ.B is scale invariant under the scale transformation r → ̺r and t → ̺ 2 t, where r = xî + yĵ + zk, ̺ is the scale factor, t is the time.…”

Section: Scaling Anomaly Of Na Systemmentioning

confidence: 99%

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Giri

2008

Int J Theor Phys

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We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann's method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ ∈ R(mod2π). There exists a single bound state for the coupling constant η 2 ∈ [0, 1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η 2 < 0, which supports bound state making the problem re-normalizable.

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“…In classical physics the transformation related to dilation D Cl , can be shown [15,16] to be responsible for generating infinitesimal scale transformation.…”

Section: Anomalous Symmetry Breakingmentioning

confidence: 99%

Conformal Anomaly in Non-Hermitian Quantum Mechanics

Giri

2010

Int. J. Mod. Phys. A

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A model of an electron and a Dirac monopole interacting through an axially symmetric nonhermitian but PT -symmetric potential is discussed in detail. The intriguing localization of the wave-packet as a result of the anomalous breaking of the scale symmetry is shown to provide a scale for the system. The symmetry algebra for the system, which is the conformal algebra SO(2, 1), is discussed and is shown to belong to the enveloping algebra of the combined algebra, composed of the Virosoro algebra, {Ln, n ∈ N} and an abelian algebra, {Pn, n ∈ N}.

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Mechanical similarity as a generalization of scale symmetry

Cited by 4 publications

References 27 publications

(2+1)D exotic Newton–Hooke symmetry, duality and projective phase

(2+1)D exotic Newton–Hooke symmetry, duality and projective phase

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Conformal Anomaly in Non-Hermitian Quantum Mechanics

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