A Pedestrian Approach to Quantum Field Theory

Harris, Edward F.; Hammer, C. L.

doi:10.1119/1.1987263

Cited by 26 publications

(50 citation statements)

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“…(1a)] is still independent of θ i ; hence, it is most easily found for the limit case of θ i ¼ 0, where our incoming electron state jp cyl i i reduces to a plane wave (a single momentum state p i ¼ βE i =c), and the radiation spread angle is just θ ph ¼ θČ R (black dashed line). Then, θČ R is found analytically from elementary conservation laws, as was first shown by Sokolov [41], and later by Cox [49] and many others [26][27][28]42,43]:…”

Section: Quantum Derivation: the Matrix Elementmentioning

confidence: 99%

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Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum

et al. 2016

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We show that the well-known Čerenkov effect contains new phenomena arising from the quantum nature of charged particles. The Čerenkov transition amplitudes allow coupling between the charged particle and the emitted photon through their orbital angular momentum and spin, by scattering into preferred angles and polarizations. Importantly, the spectral response reveals a discontinuity immediately below a frequency cutoff that can occur in the optical region. Near this cutoff, the intensity of the conventional Čerenkov radiation (ČR) is very small but still finite, while our quantum calculation predicts exactly zero intensity above the cutoff. Below that cutoff, with proper shaping of electron beams (ebeams), we predict that the traditional ČR angle splits into two distinctive cones of photonic shockwaves. One of the shockwaves can move along a backward cone, otherwise considered impossible for conventional ČR in ordinary matter. Our findings are observable for ebeams with realistic parameters, offering new applications including novel quantum optics sources, and opening a new realm for Čerenkov detectors involving the spin and orbital angular momentum of charged particles.

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Section: Quantum Derivation: the Matrix Elementmentioning

confidence: 99%

“…[25][26][27][28][29][41][42][43]). They always considered the particle as a single momentum state, analogous to a plane wave in space.…”

Section: Conventional Theory Of the čErenkov Effectmentioning

confidence: 99%

Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum

et al. 2016

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“…where ψ µ (q) = u µ (q)e ıq·x and u µ (q) are four-component spinors of the Dirac equation with corresponding eigenvalues E q = ± h 2 c 2 q 2 + m 2 c 4 and normalization u † µ (q)u ν (q) = δ µν [54]. Here, the operator c µ (q , t) annihilates a particle with momentumhq.…”

Section: Dissipative Dirac Fieldmentioning

confidence: 99%

“…We assume here, the particle with mass m is moving in an anisotropic dissipative medium. This model can be applied to the problem of Cherenkov radiation in presence of a polarizable medium [54,55]. We set V (q) = 0 in the equation (30) and find…”

Section: Free Particlementioning

confidence: 99%

Relativistic and Non-Relativistic Quantum Brownian Motion in an Anisotropic Dissipative Medium

Amooghorban

Kheirandish²

2014

Int J Theor Phys

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Using a minimal-coupling-scheme we investigate the quantum Brownian motion of a particle in an anisotropic-dissipative-medium under the influence of an arbitrary potential in both relativistic and non-relativistic regimes. A general quantum Langevin equation is derived and explicit expressions for quantum-noise and dynamical variables of the system are obtained. The equations of motion for the canonical variables are solved explicitly and an expression for the radiation-reaction of a charged particle in the presence of a dissipative-medium is obtained. Some examples are given to elucidate the applicability of this approach.

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“…Now, following Harris [12], we show, using the second quantization method how to derive theČerenkov effect in a dielectric medium characterized by its dielectric constant ε(ω) and its index of refraction n, which is given by relation √ εµ where µ is the magnetic permeability.…”

Section: The Quantum Theory Of Thečerenkov Effectmentioning

confidence: 99%