Anomalies in conservation laws in the Hamiltonian formalism

Esteve, J. G.

doi:10.1103/physrevd.34.674

Cited by 55 publications

(71 citation statements)

References 11 publications

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“…We immediately notice that (25) are not square integrable functions in phase space, which implies that d ± are zero. This proves that H is self-adjoint and, as a consequence, that there are no anomalies as explained by Esteve [14].…”

Section: Now Let Us Study What Happens When We Implement Classical Mesupporting

confidence: 61%

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Scale symmetry in classical and quantum mechanics

Gozzi

Mauro

2005

Physics Letters A

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Section: Now Let Us Study What Happens When We Implement Classical Mesupporting

confidence: 61%

“…r. It is easy to prove that these transformations on p and r can be generated via the Poisson brackets by the dilation charge D of Eq. (14). This means that the scale symmetry can be implemented as a canonical transformation in the standard phase space of classical mechanics.…”

Section: Scale Symmetry In Classical Mechanicsmentioning

confidence: 99%

Scale symmetry in classical and quantum mechanics

Gozzi

Mauro

2005

Physics Letters A

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“…This is evident by the appearance of the momentum dependence of phase shifts in the scattering sector and by the appearance of bound states in certain cases. The underlying reason behind this is that the domain of self-adjointness of the associated Hamiltonian is not kept invariant by the scaling operator [19,20,21,22]. Scale invariance at the quantum level is recovered only for special choices of the parameter z.…”

Section: Introductionmentioning

confidence: 99%

Novel quantum states of the rational Calogero models without the confining interaction

2003

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We show that the N -particle A N −1 and B N rational Calogero models without the harmonic interaction admit a new class of bound and scattering states. These states owe their existence to the self-adjoint extensions of the corresponding Hamiltonians, labelled by e iz where z ∈ R (mod 2π). It is shown that the new states appear for all values of N and for specific ranges of the coupling constants. Moreover, they are shown to exist even in the excited sectors of the Calogero models. The self-adjoint extension generically breaks the classical scaling symmetry, leading to quantum mechanical scaling anomaly. The scaling symmetry can however be restored for certain values of the parameter z. We also generalize these results for many particle systems with classically scale invariant long range interactions in arbitrary dimensions.

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“…For x → −∞, we must have Ψ(x) → 0. With that in mind we get the zero energy solution ("bound state") Ψ(x) = e mx 1 0 , (3.15) 16) which is localised near x = 0. Besides this normalisable solution, H has a set of generalised eigenfunctions.…”

Section: Remarkmentioning

confidence: 99%

Edge states: topological insulators, superconductors and QCD chiral bags

Asorey

Balachandran

Pérez-Pardo

2013

J. High Energ. Phys.

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The dynamics of the magnetic field in a superconducting phase is described by an effective massive bosonic field theory. If the superconductor is confined in a domain M with boundary ∂M , the boundary conditions of the electromagnetic fields are predetermined by physics. They are time-reversal and also parity invariant for adapted geometry. They lead to edge excitations while in comparison, the bulk energies have a large gap. A similar phenomenon occurs for topological insulators where appropriate boundary conditions for the Dirac Hamiltonian also lead to similar edge states and an "incompressible bulk". They give spin-momentum locking as well. In addition time-reversal and parity invariance emerge for adapted geometry. Similar edge states appear in QCD bag models with chiral boundary conditions.

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Anomalies in conservation laws in the Hamiltonian formalism

Cited by 55 publications

References 11 publications

Scale symmetry in classical and quantum mechanics

Scale symmetry in classical and quantum mechanics

Novel quantum states of the rational Calogero models without the confining interaction

Edge states: topological insulators, superconductors and QCD chiral bags

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