Static forces and virtual-particle exchange: Difference between revisions

Revision as of 13:35, 15 May 2019

Revision as of 11:51, 29 July 2019

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{{Use American English|date = February 2019}}

{{Short description|Physical interaction in post-classical physics}}

'''Static force fields''' are fields, such as a simple [[Electric field|electric]], [[Magnetic field|magnetic]] or [[gravitational field]]s, that exist without excitations. The [[Perturbation theory (quantum mechanics)|most common approximation method]] that physicists use for [[Scattering theory|scattering calculations]] can be interpreted as static forces arising from the interactions between two bodies mediated by '''[[virtual particle]]s''', particles that exist for only a short time determined by the [[uncertainty principle]].<ref>{{cite journal|last1=Jaeger|first1=Gregg|title=Are virtual particles less real?|journal=Entropy |volume=21 |issue=2|page=141|date=2019|urldoi=https://www10.mdpi.com3390/1099-4300/21/2/141e21020141}}</ref> The virtual particles, also known as [[force carrier]]s, are [[boson]]s, with different bosons associated with each force.<ref>{{cite book | author=A. Zee | title=Quantum Field Theory in a Nutshell| publisher= Princeton University| year=2003 | isbn=0-691-01019-6}} pp. 16-37</ref>

The virtual-particle description of static forces is capable of identifying the spatial form of the forces, such as the inverse-square behavior in [[Newton's law of universal gravitation]] and in [[Coulomb's law]]. It is also able to predict whether the forces are attractive or repulsive for like bodies.

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[[Image:101005 energy by theta.jpg|thumb|250px|right|Figure 3. Interaction energy vs. r for various values of theta. The lowest energy is for <math>\theta = {\pi\over 4 }</math> or <math> { \mathit l \over \mathit l^{\prime} } = 1 </math>. The highest energy plotted is for <math>\theta = 0.90{\pi\over 4 }</math>. Lengths are in units of <math>r_{\mathit l \mathit l^{\prime}}</math>.]]

[[Image:101011 energy picture.jpg|thumb|250px|right|Figure 4. Ground state energies for even and odd values of angular momenta. Energy is plotted on the vertical axis and r is plotted on the horizontal. When the total angular momentum is even, the energy minimum occurs when <math> { \mathit l = \mathit l^{\prime} } </math> or <math> { \mathit l \over \mathit l^{*} } = {1 \over 2} </math>. When the total angular momentum is odd, there are no integer values of angular momenta that will lie in the energy minimum. Therefore, there are two states that lie on either side of the minimum. Because <math> { \mathit l \ne \mathit l^{\prime} } </math>, the total energy is higher than the case when <math> { \mathit l = \mathit l^{\prime} } </math> for a given value of <math> { \mathit l^{*} } </math>.]]

Unlike classical currents, quantum current loops can have various values of the [[Larmor radius]] for a given energy.<ref>{{cite book | author=Z. F. Ezewa | title=Quantum Hall Effects, Second Edition| publisher= World Scientific| year=2008 | isbn=978-981-270-032-32}} pp. 187-190</ref> [[Landau level]]s, the energy states of a charged particle in the presence of a magnetic field, are multiply [[Degenerate energy level|degenerate]]. The current loops correspond to [[angular momentum]] states of the charged particle that may have the same energy. Specifically, the charge density is peaked around radii of

:<math>