Scale symmetry in classical and quantum mechanics

Gozzi, E.; Mauro, D.

doi:10.1016/j.physleta.2005.07.038

Cited by 5 publications

(8 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 84%

“…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%

See 1 more Smart Citation

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Giri

2008

Int J Theor Phys

View full text Add to dashboard Cite

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.

show abstract

Section: Scaling Anomaly Of Na Systemmentioning

confidence: 84%

Section: Scaling Anomaly Of Na Systemmentioning

confidence: 99%

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Giri

2008

Int J Theor Phys

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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}.

show abstract

“…[6]). The LMS, which in classical mechanics holds for every monomial potential, turns out to be a natural generalization of the standard scale symmetry analyzed in [4]: the only difference is that in the LMS the variables are not transformed according to their physical dimensions like in the scale transformations. We will also prove in Secs.…”

Section: Introductionmentioning

confidence: 99%

“…In this case the KvN states become ψ( r, λ p ). They evolve with the equation of motion (3) or via the following kernel of propagation: [4]:…”

Section: Introductionmentioning

confidence: 99%

Mechanical similarity as a generalization of scale symmetry

Gozzi¹,

Mauro²

2006

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

In this paper we study the symmetry known [1] as mechanical similarity (LMS) and present for any monomial potential. We analyze it in the framework of the Koopman-von Neumann formulation of classical mechanics and prove that in this framework the LMS can be given a canonical implementation. We also show that the LMS is a generalization of the scale symmetry which is present only for the inverse square potential. Finally we study the main obstructions which one encounters in implementing the LMS at the quantum mechanical level.

show abstract

Scale symmetry in classical and quantum mechanics

Abstract: In this paper we address again the issue of the scale anomaly in quantum mechanical models with inverse square potential. In particular we examine the interplay between the classical and quantum aspects of the system using in both cases an operatorial approach.

Cited by 5 publications

References 22 publications

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Conformal Anomaly in Non-Hermitian Quantum Mechanics

Mechanical similarity as a generalization of scale symmetry

Contact Info

Product

Resources

About