Static forces and virtual-particle exchange: Difference between revisions

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

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

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

'''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|doi=10.3390/e21020141|pmid=33266857 |pmc=7514619 |bibcode=2019Entrp..21..141J|doi-access=free}}</ref> The virtual particles, also known as [[force carrier]]s, are [[boson]]s, with different bosons associated with each force.<ref name="Zee">{{cite book | first = A. | last = Zee | title=Quantum Field Theory in a Nutshell| publisher= Princeton University| year=2003 | isbn=0-691-01019-6}}</ref>{{rp|pp=16–37}}

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.

The [[path integral formulation]] is the natural language for describing force carriers. This article uses the path integral formulation to describe the force carriers for [[Spin (particle physics)|spin]] 0, 1, and 2 fields. [[Pion]]s, [[photon]]s, and [[graviton]]s fall into these respective categories.

There are limits to the validity of the virtual particle picture. The virtual-particle formulation is derived from a method known as [[perturbation theory]] which is an approximation assuming interactions are not too strong, and was intended for scattering problems, not bound states such as atoms. For the strong force binding [[quark]]s into [[nucleon]]s at low energies, perturbation theory has never been shown to yield results in accord with experiments,<ref>{{cite web |url=http://www.hep.phy.cam.ac.uk/theory/research/hadronic.html |title=High Energy Physics Group - Hadronic Physics |accessdate=2010-08-31 |url-status=dead |archiveurl=https://web.archive.org/web/20110717002648/http://www.hep.phy.cam.ac.uk/theory/research/hadronic.html |archivedate=2011-07-17 }}</ref> thus, the validity of the "force-mediating particle" picture is questionable. Similarly, for [[bound state]]s the method fails.<ref>{{cite web| url=http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/Time_Ind_PT.htm|title=Time-Independent Perturbation Theory| work=virginia.edu}}</ref> In these cases, the physical interpretation must be re-examined. As an example, the calculations of atomic structure in atomic physics or of molecular structure in quantum chemistry could not easily be repeated, if at all, using the "force-mediating particle" picture.{{factcitation needed|date=October 2014}}

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<!-- Additionally, one should look critically{{fact|date=October 2014}} at the recent CERN experiments{{fact|date=October 2014}} in which evidence is shown supporting the physical reality of the Higgs boson, which is a force-mediating particle. One should be careful not to make the logical error known as [[Reification (fallacy)|reification]], which confuses concept and reality. -->

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===The Yukawa potential: The force between two nucleons in an atomic nucleus===

Consider the [[Spin (particle physics)|spin]]-0 Lagrangian density<ref name="Zee"/>{{rp|pp=21–29}}

<math display="block">

\mathcal{L} [\varphi (x)]

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====The Coulomb potential in a vacuum====

Consider the [[Spin (particle physics)|spin]]-1 [[Proca action|Proca Lagrangian]] with a disturbance<ref name="Zee"/>{{rp|pp=30–31}}

<math display="block">\mathcal{L} [\varphi (x)] = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \frac{1}{2} m^2 A_{\mu} A^{\mu} + A_{\mu} J^{\mu}</math>

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===Gravitation===

A gravitational disturbance is generated by the [[stress–energy tensor]] <math> T^{\mu \nu} </math>; consequently, the Lagrangian for the gravitational field is [[Spin (particle physics)|spin]]-2. If the disturbances are at rest, then the only component of the stress–energy tensor that persists is the <math> 00 </math> component. If we use the same trick of giving the [[graviton]] some mass and then taking the mass to zero at the end of the calculation the propagator becomes

<math display="block">D\left ( k \right )\mid_{k_0=0}\; = \; - \frac{4}{3} \frac{1}{\vec k^2 + m^2}</math>

and