Soft boson radiation and fractal probability distributions

Widom, A.; Kidambi, V.; Srivastava, Y. N.

doi:10.1063/1.58297

Cited by 5 publications

(3 citation statements)

References 1 publication

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“…Experimental examples of physical systems which can be usefully described by coordinates in the non-commutative plane include the following: (i) vortices in superfluid 4 He films [3], (ii) quantum Hall effect charged magnetic vortices in two-dimensional electron liquids [4], (iii) quantum interference phase between two alternative paths in the plane (as in the Aharonov-Bohm effect) [2] and (iv) high energy charged lepton beams stored in cyclotrons [5,6,7]. In all of these experimental examples, there exists the ordinary Euclidean geometry of position vectors (r 1 , r 2 , .…”

Section: Introductionmentioning

confidence: 99%

Non-commutative geometry and measurements of polarized two photon coincidence counts

et al. 2004

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Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon "Zitterbewegung" along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described.

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Section: Introductionmentioning

confidence: 99%

Non-commutative geometry and measurements of polarized two photon coincidence counts

et al. 2004

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“…The necessity for a consistent Dirac equation in a medium has been recognized in the literature within the context of neutrino oscillations in the medium [10][11][12][13]. In particular, in references [10,11] a proposal for a fieldtheoretical treatment of neutrino oscillations in the medium starting from the Dirac equation was presented.…”

Section: Introductionmentioning

confidence: 99%

Fermion damping in a fermion-scalar plasma

et al. 1999

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In this article we study the dynamics of fermions in a fermion-scalar plasma. We begin by obtaining the effective in-medium Dirac equation in real time which is fully renormalized and causal and leads to the initial value problem. For a heavy scalar we find the novel result that the decay of the scalar into fermion pairs in the medium leads to damping of the fermionic excitations and their in-medium propagation as quasiparticles. That is, the fermions acquire a width due to the decay of the heavier scalar in the medium. We find the damping rate to lowest order in the Yukawa coupling for arbitrary values of scalar and fermion masses, temperature and fermion momentum. An all-order expression for the damping rate in terms of the exact quasiparticle wave functions is established. A kinetic Boltzmann approach to the relaxation of the fermionic distribution function confirms the damping of fermionic excitations as a consequence of the induced decay of heavy scalars in the medium. A linearization of the Boltzmann equation near equilibrium clearly displays the relationship between the damping rate of fermionic mean fields and the fermion interaction rate to lowest order in the Yukawa coupling directly in real time. 12.15Ji,12.38.Mh

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“…[17,18] conclude that the concept of wave packet is unnecessary for all the relevant physical cases. A bunch of other methods has also been discussed [7,16,17,19,20] (to name a few).…”

Section: Introductionmentioning

confidence: 99%

Neutrino propagation in matter using the wave packet approach

Peltoniemi

Sipilainen

2000

J. High Energy Phys.

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We study the oscillations and conversions of relativistic neutrinos propagating in matter of variable density using the wave packet formalism. We show how the oscillation and coherence lengths are modified in comparison with the case of oscillations in vacuum. Secondly, we demonstrate how the equation of motion for two neutrino flavors can be formally solved for almost arbitrary density profile. We calculate finally how the use of wave packets alters the nonadiabatic level crossing probabilities. For the most common physical environments the corrections due to the width of the wave packet do not lead to observable effects.Recent experimental discoveries [1] seem to suggest that neutrino oscillations [2,3,4,5] really exist. Since the observation of neutrino oscillation may provide valuable information on the basic properties of neutrinos, e.g. masses and mixing angles, it is important to know the underlying physics also on the conceptual level.It was pointed out e.g. in Refs.[6] and [7] that the standard quantum mechanical treatment of neutrino oscillations using plane waves [5,8] is not completely satisfactory for many reasons. The wave packet approach [6],[9]-[15] provides a more physical picture which is particularly adapted for describing phenomena localized in space and time. This formalism also elegantly accounts for the loss of coherence by the separation of wave packets. However, some authors (e.g. [7,16,17]) have been skeptical about the use of wave packets, and Refs. [17,18] conclude that the concept of wave packet is unnecessary for all the relevant physical cases. A bunch of other methods has also been discussed [7,16,17,19,20] (to name a few).In this paper we will consider neutrino oscillations and other phenomena in matter. We have decided to use wave packets because the calculations of the kind presented here have never been carried out before.We will first focus on the equation of motion for neutrinos propagating in matter of variable density. Generally the equation is modified in matter due to coherent forward scatterings [21,22,23,24], and an exact solution can be found only for few special cases. Here we address one special case where the density of matter changes slowly enough, so that the situation is said to be adiabatic. Now the eigensolutions for the equation of motion are found trivially, for arbitrary number of relativistic neutrinos. To describe neutrino oscillations in matter, we apply the method of Ref. [14] in connection with these solutions. We can express the results formally using effective oscillation and coherence lengths which are not local quantities anymore.Generally neutrinos may propagate nonadiabatically, and solving the complete equation of motion even for two neutrino flavors is usually far from trivial (see e.g. [25,26,27] for two specific density profiles). In this paper we show that the solution for "arbitrary" density profile can be constructed by using infinite integral series. Some supplementary calculations which may be of formal interest are enclosed in Appendix B...

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Soft boson radiation and fractal probability distributions

Cited by 5 publications

References 1 publication

Non-commutative geometry and measurements of polarized two photon coincidence counts

Non-commutative geometry and measurements of polarized two photon coincidence counts

Fermion damping in a fermion-scalar plasma

Neutrino propagation in matter using the wave packet approach

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