Five momenta

Berry, Michael

doi:10.1088/0143-0807/34/6/1337

Cited by 47 publications

(47 citation statements)

References 30 publications

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“…In the main part of this work we consider the complex electric-field amplitude E(r) of a monochromatic optical field, although the approach of this subsection applies to any complex multi-component field E = (E 1 , ..., E n ). On the one hand, a straightforward extension of the above scalar-field equations allows the introduction of the local wavevector (canonical momentum density) as the weighted average of the local wavevectors for each field component: [63][64][65][66]. However, unlike Eq.…”

Section: Introductionmentioning

confidence: 99%

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

2019

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Geometric phases are a universal concept that underpins numerous phenomena involving multicomponent wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem.Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincaré sphere and the Majoranasphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization Möbius strips.

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Section: Introductionmentioning

confidence: 99%

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

2019

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“…There have been in recent years a growing number of works [43][44][45][46][47] which consider inferring weak values using (strong) projective measurements [48,49], yet not with full generality. In this paper we prove via a new and general protocol that both the real and imaginary parts of weak values can be obtained in principle through strong projective measurements.…”

Section: Introductionmentioning

confidence: 99%

Determination of weak values of quantum operators using only strong measurements

Cohen

Pollak

2018

Phys. Rev. A

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Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux and hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements implying that weak values are general properties of operators in association with pre-and post-selection and they need not be preferentially associated with weak measurements. They should be considered as an important measurable property which provides added information as compared with the "standard" diagonal expectation value of an operator. As a first specific example we consider the determination of the real and imaginary parts of the weak value of the momentum operator employing projective time of flight experiments. Then the results are analyzed from the point of view of Bohmian mechanics. Finally we consider recent neutron interferometry experiments used to determine the weak values of the neutron spin.

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“…Even massless waves in 3D can propagate with the speed of light along the z -axis only if these are delocalized in the transverse plane. In contrast, the modified boost eigenmodes (14), (32), (33) considered in [25][26][27][28] are non-divergent, but propagate with significant shape deformations. In any case, for causal signal propagation in the massive Klein-Gordon equation, there is always a Sommerfeld precursor, which propagates exactly with the speed of light (although the main part of the signal propagates with a subluminal group velocity) [19][20][21].…”

Section: Discussionmentioning

confidence: 99%

“…2b. Note that, considering the particle current and density as "local wavevector" and "local frequency" [32], the local phase velocity is given by their ratio, and its absolute value always equals to the speed of light. This is in contrast to the superluminal phase velocity of plane waves (5) [21].…”

Section: Particle Density Current and Fourier Spectrummentioning

confidence: 99%

Lorentz-boost eigenmodes

Bliokh

2018

Phys. Rev. A

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Plane waves and cylindrical or spherical vortex modes are important sets of solutions of quantum and classical wave equations. These are eigenmodes of the energymomentum and angular-momentum operators, i.e., generators of spacetime translations and spatial rotations, respectively. Here we describe another set of wave modes: eigenmodes of the "boost momentum" operator, i.e., a generator of Lorentz boosts (spatio-temporal rotations). Akin to the angular momentum, only one (say, z ) component of the boost momentum can have a well-defined quantum number. The boost eigenmodes exhibit invariance with respect to the Lorentz transformations along the z -axis, leading to scale-invariant wave forms and step-like singularities moving with the speed of light. We describe basic properties of the Lorentz-boost eigenmodes and argue that these can serve as a convenient basis for problems involving causal propagation of signals.

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Five momenta

Cited by 47 publications

References 30 publications

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Determination of weak values of quantum operators using only strong measurements

Lorentz-boost eigenmodes

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