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Virtual photons are off-mass-shell quantum fluctuations in gauge fields
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SUPPORTED
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Retrieved physics literature confirms that virtual particles and force-mediating quanta in quantum field theory are characterized as being off the mass shell.

Evidence for · 3
2019 · cited by 39
The question of whether virtual quantum particles exist is considered here in light of previous critical analysis and under the assumption that there are particles in the world as described by quantum field theory. The relationship of the classification of particles to quantum-field-theoretic calculations and the diagrammatic aids that are often used in them is clarified. It is pointed out that the distinction between virtual particles and others and, therefore, judgments regarding their reality have been made on basis of these methods rather than on their physical characteristics. As such, it has obscured the question of their existence. It is here argued that the most influential arguments against the existence of virtual particles but not other particles fail because they either are arguments against the existence of particles in general rather than virtual particles per se, or are dependent on the imposition of classical intuitions on quantum systems, or are simply beside the point. Several reasons are then provided for considering virtual particles real, such as their descriptive, explanatory, and predictive value, and a clearer characterization of virtuality—one in terms of intermediate states—that also applies beyond perturbation theory is provided. It is also pointed out that in the role of force mediators, they serve to preclude action-at-a-distance between interacting particles. For these reasons, it is concluded that virtual particles are as real as other quantum particles. [ 9 ] (Section 1.3) and the comments of Steven Weinberg near the end of the following section). 2. The Real/Virtual Distinction and its Limits The distinction between virtual quanta and other quanta is standardly made in a very specific way: the virtual particles are those that appear as “internal lines” of the Feynman diagrams; and any particle not eventually It is also sometimes, though less often, taken instead as the distinguishing characteristic of a virtual particle that it be “off mass-shell”, that is, that it have a mass not corresponding to the value standardly attributed to the corresponding quantum and, so, be a virtual version of that quantum. This may or may not coincide with its being symbolized by an internal line in perturbation-theoretical diagrams and is also a consequence of electing a particular mathematical method of analysis, that of Feynman himself—this is discussed near the end of Section 5 , below. Alternatively, the mass can be taken to be fixed at its standard value, the corresponding energy-momentum relation— E 2 = p 2 + m 2 , where p is momentum, m is mass, and c = 1 —may be considered not to be satisfied at the diagrammatic vertices, as discussed in greater detail in Section 5 , below, instead of enforcing this relation. (It is because this equation is that of a sphere that particles not satisfying it are considered off shell, that is, off that sphere). It is, therefore, sometimes instead (incorrectly) concluded that virtual particles violate the conservation of energy. The consideration of quanta as off mass-shell, like the perturbation-theoretical calculations in which it arises, is therefore a matter of the choice of method of analysis of interaction and, more importantly, neither of the above alternatives requires the rejection of virtual quanta as quanta, that is, to consider them not to exist in the sense I am arguing here that they do. The most influential argument against the reality of virtual particles, which has come to be known as the “superposition argument”, is that virtual particles do not exist because neither the number nor kinds of virtual particles are determinate during scattering processes as modeled by quantum field theory—cf. The following commentary from Steven Weinberg’s 1977 article “A Search for Unity: Notes for a History of Quantum Field Theory” indicates the significance of the introduction of virtual particles by quantum field theory and addresses this as well as the issue of energy conservation: “It is important to understand that quantum field theory gave rise to a new view not only of particles but also of the forces among them. We can think of two charged particles interacting at a distance not by creating classical electromagnetic fields which act on one another, but by exchanging photons, which continually pass from one particle to the other. Thus, all observed phenomena of particle physics can, within the constraints of such approximations, be related to the quantum fields appearing in theory through experiments involving standard preparation and detection procedures and will involve (virtual quanta of) force-mediating fields. However, for example, analyses of effects involving collections of virtual particles giving rise to mass- and charge-value corrections—in which there are an infinite number of perturbation-theoretical contributions wherein more than one of them contributes significantly—are far less susceptible to such intuitive, quasi-physical misinterpretation but still involve intermediate quantum states including such quanta. The virtual particle mass becomes a variable of integration (cf., [ 34 ]) and the particle is said to be “off mass-shell,” which as mentioned previously is for some an alternative indication of virtuality; any difference of mass of virtual particles from standard values in intermediate states is not physically problematic but only requires caution against incorrectly attributing the free-state values of masses given to particles while they are in those short-lived states. Under this more objective characterization, virtual particles are as real as all others. One may note also that one method of non-perturbative field theory, lattice quantum chromodynamics, treats virtual particles differently from others, as “links” between sites of a discrete space-time lattice at which interacting particles are located, (in the limit taken) infinitesimally closely without a finite interval in which to propagate.
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rails:sufficiency:supported:single_source:for=1+2p:against=0+0p | v55:sufficiency

More for · 2
2020 · cited by 6
The anomalous nanoscale electromagnetic field arising from light–matter interactions in a nanometric space is called a dressed photon. While the generic technology realized by utilizing dressed photons has demolished the conventional wisdom of optics, for example, the unexpectedly high-power light emission from indirect-transition type semiconductors, dressed photons are still considered to be too elusive to justify because conventional optical theory has never explained the mechanism causing them. The situation seems to be quite similar to that of the dark energy/matter issue in cosmology. Regarding these riddles in different disciplines, we find a common important clue for their resolution in the form of the relevance of space-like momentum support, without which quantum fields cannot interact with each other according to a mathematical result of axiomatic quantum field theory. Here, we show that a dressed photon, as well as dark energy, can be explained in terms of newly identified space-like momenta of the electromagnetic field and dark matter can be explained as the off-shell energy of the Weyl tensor field.
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approximation are always virtual, i.e. transient quantum field fluctuations, one understands why the running of a coupling is a genuine quantum and relativistic In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling) is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, w… In field theory, V {\displaystyle V} always contains 3 fields terms or more, expressing for example that an initial electron (field 1) interacts with a photon (field 2) producing the final state of the electron (field 3). In contrast, the kinetic part T {\displaystyle T} always contains only two fields, expressing the free propagation of an initial particle (field 1) into a later state (field 2). The coupling constant determines the magnitude of the T {\displaystyle T} part with respect to the V {\displaystyle V} part (or between two sectors of the interaction part if several fields that couple differently are present). For example, the electric charge of a particle is a coupling constant that characterizes an interaction with two charge-carrying fields and one photon field (hence the common Feynman diagram with two arrows and one wavy line). Since photons mediate the electromagnetic force, this coupling determines how strongly electrons feel such a force, and has its value fixed by experiment. In the motion of a large lump of magnetized iron, the magnetic forces may be more important than the gravitational forces because of the relative magnitudes of the coupling constants. However, in classical mechanics, one usually makes these decisions directly by comparing forces. Another important example of the central role played by coupling constants is that they are the expansion parameters for first-principle calculations based on perturbation theory, which is the main method of calculation in many branches of physics. == Fine-structure constant == Couplings arise naturally in a quantum field theory. A special role is played in relativistic quantum theories by couplings that are dimensionless; i.e., are pure numbers. An example of such a dimensionless constant is the fine-structure constant, α = e 2 4 π ε 0 ℏ c , {\displaystyle \alpha ={\frac {e^{2}}{4\pi \varepsilon _{0}\hbar c}},} where e is the charge of an electron, ε0 is the permittivity of free space, ħ is the reduced Planck constant and c is the speed of light. This constant is proportional to the square of the coupling strength of the charge of an electron to the electromagnetic field. In quantum field theory, the dimension of the coupling plays an important role in the renormalizability property of the theory, and therefore on the applicability of perturbation theory. If the coupling is dimensionless in the natural units system (i.e. c = 1 {\displaystyle c=1} , ℏ = 1 {\displaystyle \hbar =1} ), like in QED, QCD, and the weak interaction, the theory is renormalizable and all the terms of the expansion series are finite (after renormalization). If the coupling is dimensionful, as e.g. in gravity ( [ G N ] = energy − 2 {\displaystyle [G_{N}]={\text{energy}}^{-2}} ), the Fermi theory ( [ G F ] = energy − 2 {\displaystyle [G_{F}]={\text{energy}}^{-2}} ) or the chiral perturbation theory of the strong force ( [ F ] = energy {\displaystyle [F]={\text{energy}}} ), then the theory is usually not renormalizable. Perturbation expansions in the coupling might still be feasible, albeit within limitations, as most of the higher order terms of the series will be infinite. == Running coupling == One may probe a quantum field theory at short times or distances by changing the wavelength or momentum, k, of the probe used. With a high frequency (i.e., short time) probe, one sees virtual particles taking part in every process. This apparent violation of the conservation of energy may be understood heuristically by examining the uncertainty relation Δ E Δ t ≥ ℏ 2 , {\displaystyle \Delta E\Delta t\geq {\frac {\hbar }{2}},} which virtually allows such violations at short times. The foregoing remark only applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture. In other formulations, the same event is described by "virtual" particles going off the mass shell. the charges or masses are larger, or r {\displaystyle r} is smaller) or happens over briefer time spans (smaller r {\displaystyle r} ), more force carriers are involved or particle This latter is then accounted for by being included in the coupling, which then becomes 1 / r {\displaystyle 1/r} -dependent, (or equivalently μ-dependent). Since the additional particles involved beyond the single force carrier approximation are always virtual, i.e. transient quantum field fluctuations, one understands why the running of a coupling is a genuine quantum and relativistic phenomenon, namely an effect of the high-order Feynman diagrams on the strength of the force. Since a running coupling effectively accounts for microscopic quantum effects, it is often called an effective coupling, in contrast to the bare coupling (constant) present in the Lagrangian or Hamiltonian. However, one cannot expect the perturbative beta function to give accurate results at strong coupling, and so it is likely that the Landau pole is an artifact of applying perturbation theory in a situation where it is no longer valid. The true scaling behaviour of α {\displaystyle \alpha } at large energies is not known. === QCD and asymptotic freedom === In non-abelian gauge theories, the beta function can be negative, as first found by Frank Wilczek, David Politzer and David Gross. An example of this is the beta function for quantum chromodynamics (QCD), and as a result the QCD coupling decreases at high energies.
Everything we examined (3)
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  1. Coupling constantreferenceno side taken
  2. Are Virtual Particles Less Real?referenceno side taken
  3. Off-Shell Quantum Fields to Connect Dressed Photons with Cosmologypeer-reviewedno side taken
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first checked05 Aug 2026
judged → SUPPORTED · 8605 Aug 2026
held for human review09 Aug 2026
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