Quantum field theory - Revision history

DavidB4-bot: /* top */HTTP --> HTTPS #3, replaced: http://arxiv.org → https://arxiv.org (2)

2019-04-09T19:54:31Z

‎top: HTTP --> HTTPS #3, replaced: http://arxiv.org → https://arxiv.org (2)

PeterIceHockey: fied/removed red links

2016-12-14T14:07:32Z

fied/removed red links

DavidB4-bot: /* top */correcting hyphen usage, as requested, replaced: th-century → th century

2016-09-02T16:03:42Z

‎top: correcting hyphen usage, as requested, replaced: th-century → th century

DavidB4-bot: clean up & uniformity

2016-07-13T18:04:09Z

clean up & uniformity

Show changes

DavidB4-bot: Spelling, Grammar, and General Cleanup, typos fixed: labor intensive → labor-intensive, 1930's → 1930s, well-known → well known

2016-07-11T13:35:41Z

Spelling, Grammar, and General Cleanup, typos fixed: labor intensive → labor-intensive, 1930's → 1930s, well-known → well known

SamHB: "Cannot be valid" is a little harsh for something so successful. Of course it's not perfect.

2015-12-13T06:10:04Z

"Cannot be valid" is a little harsh for something so successful. Of course it's not perfect.

Aschlafly: This theory is in conflict with theories of gravitation, and thus cannot be valid. However, QFT is taught as a mathematical curiosity that can be made consistent with electromagnetic, weak nuclear, and strong nuclear forces.

2015-12-04T03:39:02Z

This theory is in conflict with theories of gravitation, and thus cannot be valid. However, QFT is taught as a mathematical curiosity that can be made consistent with electromagnetic, weak nuclear, and strong nuclear forces.

SamHB: Put sentence where it belongs.

2015-12-03T05:41:26Z

Put sentence where it belongs.

SamHB: Explain the connection with relativity a little better.

2015-12-03T05:26:25Z

Explain the connection with relativity a little better.

SamHB: "Attempts unsuccessfully"? Come on! It's arguably the most precisely verified theory in physics, and the article says so 4 paragraphs down.

2015-12-01T04:44:19Z

"Attempts unsuccessfully"? Come on! It's arguably the most precisely verified theory in physics, and the article says so 4 paragraphs down.

@@ Line 18: / Line 18: @@
 The most naive application of Quantum Field Theory to any theory of gravity is known to be unworkable. It has a well-known (in theoretical physics circles) "cosmological constant problem."<ref>
-*[http://arxiv.org/ftp/arxiv/papers/0711/0711.0220.pdf The Vacuum and the Cosmological Constant Problem]
+*[https://arxiv.org/ftp/arxiv/papers/0711/0711.0220.pdf The Vacuum and the Cosmological Constant Problem]
 *[http://www.math.columbia.edu/~woit/wordpress/?p=5327 Scrutinizing the Cosmological Constant Problem]
-*[http://arxiv.org/abs/1211.4848 Scrutinizing the Cosmological Constant Problem and a possible resolution]</ref>
+*[https://arxiv.org/abs/1211.4848 Scrutinizing the Cosmological Constant Problem and a possible resolution]</ref>
 This is in contrast to the other three forces of nature (electromagnetic, weak nuclear, strong nuclear), which have extensive and impressive experimental confirmation.<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions''; Benjamin/Cummings Co. (1983).</ref> No alternative formulations of quantum gravity have experimental confirmation. While [[Special Relativity]] is an intrinsic part of quantum field theory, the prevailing theory of gravity (the curvature of spacetime under [[General Relativity]]) has not been reconciled.  Integrating this fourth force of nature into quantum field theory is an extremely active area of theoretical research. Current research in the field involves such things as [[supersymmetry]] and [[string theory]]

@@ Line 38: / Line 38: @@
 How is it that particles affect each other—for example, the repulsion of like charges, or attraction of unlike charges?
-Field theory can incorporate "action at a distance" models by the direct incorporation of an external potential field, e.g. V(x) where x is the distance from a fixed, unmoving charge, and V is the potential energy of the interaction. However, such models are of limited use because x becomes dependent on the motion of the other particle, if the other particle moves; and in addition this method ignores fluctuations of virtual particles expected from [[Heisenberg's Uncertainty Principle]]. Thus, most commonly field theory employs other methods.
+Field theory can incorporate "action at a distance" models by the direct incorporation of an external potential field, e.g. V(x) where x is the distance from a fixed, unmoving charge, and V is the potential energy of the interaction. However, such models are of limited use because x becomes dependent on the motion of the other particle, if the other particle moves; and in addition this method ignores fluctuations of virtual particles expected from [[Uncertainty principle|Heisenberg's Uncertainty Principle]]. Thus, most commonly field theory employs other methods.
 The forces of nature are mediated by particles called field [[bosons]]. Particles exert forces on each other, which appears to be action at a distance, by passing back and forth between them virtual field bosons, which exchange their momenta.  As an analogy, consider two people on ice skates on an ice rink, playing football. The first throws a football, and the reaction force of the throw pushes him backward. The second catches the football, and the catch pushes her backward. The two ice skaters are now "repelled" and moving away from each other, with the football as mediator of the force. Thus, virtual bosons mediate attractive and repulsive forces.
@@ Line 48: / Line 48: @@
 The weak nuclear force is mediated by particles called W and Z bosons. These are very massive particles, as massive as a heavy atomic nucleus.  The W particles are charged (W+ and W-) and Z is uncharged.
-The electromagnetic and weak forces have been mathematically unified into a single formalism, called [[Electroweak Theory]].<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 6; Benjamin/Cummings Co. (1983).</ref> The unification means that photons, W and Z bosons are all considered to be different aspects of a more fundamental doublet of field bosons.  The electroweak theory can describe electromagnetic and weak phenomena with fewer tuneable free parameters—as the single most important goal of physics is to describe all forces with as few free parameters as possible. Electroweak Theory has been extremely successful, and predicted the existence and approximate mass of the Z boson before its observation in experiments.
+The electromagnetic and weak forces have been mathematically unified into a single formalism, called Electroweak Theory.<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 6; Benjamin/Cummings Co. (1983).</ref> The unification means that photons, W and Z bosons are all considered to be different aspects of a more fundamental doublet of field bosons.  The electroweak theory can describe electromagnetic and weak phenomena with fewer tuneable free parameters—as the single most important goal of physics is to describe all forces with as few free parameters as possible. Electroweak Theory has been extremely successful, and predicted the existence and approximate mass of the Z boson before its observation in experiments.
 The strong nuclear force is mediated by particles called gluons. Particles such as quarks are said to have "color charge", which gives them an ability to exchange gluons, in the same way that particles with electrical charge can exchange photons. The theory that describes quarks and gluons is called Quantum Chromodynamics, or QCD.<ref>Chris Quigg. ''Gauge Theories of the Strong, Weak, and Electromagnetic Interactions'' Chapter 8; Benjamin/Cummings Co. (1983).</ref> A major complication in QCD is that the gluons themselves have "color charge", unlike, say, photons which have no electrical charge. This makes QCD calculations extremely difficult.  On the other hand, it has the advantage of eliminating the "screening problem" identified by Landau. Also, the coupling between quarks and gluons (color charge) is, measured in absolute units, much larger than the electrical charges of charged particles like electrons.

← Older revision		Revision as of 16:03, September 2, 2016
Line 1:		Line 1:
−	'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation. In the areas of its domain (electromagnetic, weak nuclear, and strong nuclear forces), it is arguably the most precisely verified theory in all of physics. It is so close to being the "theory of everything" that it is part of the advanced physics curriculum everywhere. But since it does not integrate gravity into its formulation, it isn't actually the ultimate "theory of everything".	+	'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th century formulation. In the areas of its domain (electromagnetic, weak nuclear, and strong nuclear forces), it is arguably the most precisely verified theory in all of physics. It is so close to being the "theory of everything" that it is part of the advanced physics curriculum everywhere. But since it does not integrate gravity into its formulation, it isn't actually the ultimate "theory of everything".

	QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.		QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.

@@ Line 5: / Line 5: @@
 The differences between basic QM and Field Theory are these: in QM, the interactions between more than two particles are increasingly difficult to model, and the creation and destruction of particles cannot be modeled at all. In contrast, Field Theory can describe states containing arbitrary numbers of particles of different energies, masses, charges and types. Field Theory also provides an elegant framework for describing the interactions between particles, and the creation of new particles and destruction of old ones-- for example, the emission and absorption of photons by electrons, and vice versa.<ref>Bjorken and Drell. <i>Quantum Field Theory</i> Chapter 3; McGraw Hill Inc. (1980)</ref>
-Like all physical theories since the mid-1930's, QFT is "Lorentz invariant".  That is, it is consistent with [[Theory of Relativity|Special Relativity]].  However, as discussed below, it does not explain gravity in a manner consistent with the curvature of spacetime in General Relativity.
+Like all physical theories since the mid-1930s, QFT is "Lorentz invariant".  That is, it is consistent with [[Theory of Relativity|Special Relativity]].  However, as discussed below, it does not explain gravity in a manner consistent with the curvature of spacetime in General Relativity.
 QFT bases the mathematical work on an assumption that elementary particles can be treated as "point-like objects of zero intrinsic size."<ref>http://theory.caltech.edu/people/jhs/strings/str114.html</ref>
@@ Line 29: / Line 29: @@
 The electromagnetic force models interactions between electrically charged particles, and historically resulted from a unification of the electrical and magnetic fields, which were once thought to be separate fields.
-The weak nuclear force<ref>Chris Quigg. <i>Gauge Theories of the Strong, Weak, and Electromagnetic Interactions</i> Chapter 6; Benjamin/Cummings Co. (1983).</ref> is most well-known for mediating radioactive atomic decays, in which (for example) a proton in a nucleus will turn into a neutron (which remains in the nucleus), and a positron and neutrino, which are emitted. Non-nuclear particles such as electrons also participate in the weak force. Neutrinos only participate in the weak force, and have extremely low mass, making their observation very difficult. The weak nuclear force only exerts force when particles are extremely close together.
+The weak nuclear force<ref>Chris Quigg. <i>Gauge Theories of the Strong, Weak, and Electromagnetic Interactions</i> Chapter 6; Benjamin/Cummings Co. (1983).</ref> is most well known for mediating radioactive atomic decays, in which (for example) a proton in a nucleus will turn into a neutron (which remains in the nucleus), and a positron and neutrino, which are emitted. Non-nuclear particles such as electrons also participate in the weak force. Neutrinos only participate in the weak force, and have extremely low mass, making their observation very difficult. The weak nuclear force only exerts force when particles are extremely close together.
 The strong nuclear force holds together the protons and neutrons in an atomic nucleus, and the quarks within protons, neutrons, and mesons.<ref>Chris Quigg. <i>Gauge Theories of the Strong, Weak, and Electromagnetic Interactions</i> Chapter 8; Benjamin/Cummings Co. (1983).</ref>  Because protons all have the same charge, they repel each other strongly, and the strong nuclear force is necessary to overcome this and hold them together in a nucleus; likewise for the quarks inside protons, neutrons and mesons. Unlike electromagnetism, which can extend over long distances, the strong nuclear force only exerts force when particles are extremely close together; but at close range, it is enormously stronger than electromagnetism.
@@ Line 66: / Line 66: @@
 Calculations involving field theory are universal throughout high-energy particle physics.  Here we will briefly summarize a few more notable successes.
-As stated above, one the greatest achievements of QED is the very labor intensive, but extremely precise, calculation of the angular magnetic moment of the electron. In classical quantum mechanics, the magnetic moment of the electron, called <i>g</i>, should be exactly 2.0.  The very small deviation from 2 is called the anomalous magnetic moment, and can be experimentally measured to extremely high precision.  The very labor-intensive theoretical predictions<ref>G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, ''New Determination of the Fine Structure Constant from the Electron g Value and QED,'' Phys. Rev. Lett. 97, 030802 (2006), Erratum, Phys. Rev. Lett. 99, 039902 (2007).</ref> from QED match the experimental measurement to one part in a billion<ref>B. Odom, D. Hanneke, B. D'Urso, and G. Gabrielse, ''New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron,'' Phys. Rev. Lett. 97, 030801 (2006).</ref>, a precision unparalleled in all of science.  Also, the magnetic moment of the muon can be predicted to one part in a billion.
+As stated above, one the greatest achievements of QED is the very labor-intensive, but extremely precise, calculation of the angular magnetic moment of the electron. In classical quantum mechanics, the magnetic moment of the electron, called <i>g</i>, should be exactly 2.0.  The very small deviation from 2 is called the anomalous magnetic moment, and can be experimentally measured to extremely high precision.  The very labor-intensive theoretical predictions<ref>G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, ''New Determination of the Fine Structure Constant from the Electron g Value and QED,'' Phys. Rev. Lett. 97, 030802 (2006), Erratum, Phys. Rev. Lett. 99, 039902 (2007).</ref> from QED match the experimental measurement to one part in a billion<ref>B. Odom, D. Hanneke, B. D'Urso, and G. Gabrielse, ''New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron,'' Phys. Rev. Lett. 97, 030801 (2006).</ref>, a precision unparalleled in all of science.  Also, the magnetic moment of the muon can be predicted to one part in a billion.
 Also, as stated above, the Electroweak Theory, a unification of QED and weak force, predicted the existence and approximate mass of the Z boson before its observation.<ref>Chris Quigg. <i>Gauge Theories of the Strong, Weak, and Electromagnetic Interactions</i> Chapter 6; Benjamin/Cummings Co. (1983).</ref>

← Older revision		Revision as of 06:10, December 13, 2015
Line 1:		Line 1:
−	'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation. ~~This theory is in conflict with theories~~ of ~~gravitation, and thus cannot be valid. However, QFT is taught as a mathematical curiosity that can be made consistent with~~ electromagnetic, weak nuclear, and strong nuclear forces.	+	'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation. In the areas of its domain (electromagnetic, weak nuclear, and strong nuclear forces), it is arguably the most precisely verified theory in all of physics. It is so close to being the "theory of everything" that it is part of the advanced physics curriculum everywhere. But since it does not integrate gravity into its formulation, it isn't actually the ultimate "theory of everything".

	QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.		QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.

← Older revision		Revision as of 03:39, December 4, 2015
Line 1:		Line 1:
−	'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation. ~~In the areas~~ of ~~its domain (~~electromagnetic, weak nuclear, and strong nuclear forces~~), it is arguably the most precisely verified theory in all of physics~~.	+	'''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation. This theory is in conflict with theories of gravitation, and thus cannot be valid. However, QFT is taught as a mathematical curiosity that can be made consistent with electromagnetic, weak nuclear, and strong nuclear forces.

	QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.		QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.

@@ Line 17: / Line 17: @@
 Field theoretical calculations become increasingly difficult as the number of (incoming or outgoing) particles increases; for very large numbers of particles (e.g. macroscopic liquids and solids), the methods of [[Solid State Physics]] (also based on QM) are employed instead.
-The most naive application of Quantum Field Theory to any theory of gravity is known to be unworkable. This is in contrast to the other three forces of nature (electromagnetic, weak nuclear, strong nuclear), which have extensive and impressive experimental confirmation<ref>Chris Quigg. <i>Gauge Theories of the Strong, Weak, and Electromagnetic Interactions</i>; Benjamin/Cummings Co. (1983).</ref>. No alternative formulations of quantum gravity have experimental confirmation. While [[Special Relativity]] is an intrinsic part of quantum field theory, the prevailing theory of gravity (the curvature of spacetime under [[General Relativity]]) has not been reconciled.  Integrating this fourth force of nature into quantum field theory is an extremely active area of theoretical research. Current research in the field involves such things as [[supersymmetry]] and [[string theory]]
+The most naive application of Quantum Field Theory to any theory of gravity is known to be unworkable. It has a well-known (in theoretical physics circles) "cosmological constant problem."<ref>
-−
-In dealing with gravity, QFT has a well-known (in theoretical physics circles) "cosmological constant problem."<ref>
 *[http://arxiv.org/ftp/arxiv/papers/0711/0711.0220.pdf The Vacuum and the Cosmological Constant Problem]
 *[http://www.math.columbia.edu/~woit/wordpress/?p=5327 Scrutinizing the Cosmological Constant Problem]
 *[http://arxiv.org/abs/1211.4848 Scrutinizing the Cosmological Constant Problem and a possible resolution]</ref>
 == The Forces of Nature ==

@@ Line 1: / Line 1: @@
 '''Quantum field theory''' (QFT) is a mathematical theory in physics which modernizes [[quantum mechanics]] from its early-20th-century formulation.  In the areas of its domain (electromagnetic, weak nuclear, and strong nuclear forces), it is arguably the most precisely verified theory in all of physics.
-"Field theory" describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.
+QFT describes the interactions between subatomic particles, such as electrons, protons, quarks and photons.
 The differences between basic QM and Field Theory are these: in QM, the interactions between more than two particles are increasingly difficult to model, and the creation and destruction of particles cannot be modeled at all. In contrast, Field Theory can describe states containing arbitrary numbers of particles of different energies, masses, charges and types. Field Theory also provides an elegant framework for describing the interactions between particles, and the creation of new particles and destruction of old ones-- for example, the emission and absorption of photons by electrons, and vice versa.<ref>Bjorken and Drell. <i>Quantum Field Theory</i> Chapter 3; McGraw Hill Inc. (1980)</ref>
-QFT assumes that relativity is true, and then bases the mathematical work on an assumption that elementary particles can be treated as "point-like objects of zero intrinsic size."<ref>http://theory.caltech.edu/people/jhs/strings/str114.html</ref>
+Like all physical theories since the mid-1930's, QFT is "Lorentz invariant".  That is, it is consistent with [[Theory of Relativity|Special Relativity]].  However, as discussed below, it does not explain gravity in a manner consistent with the curvature of spacetime in General Relativity.
 For a given interaction of particles, field theoretical calculations generally cannot be solved in a closed, analytical form-- that is, the predicted probabilities cannot be described by one simple equation; however, physicists have developed numerous approximation methods which produce estimates of ever-increasing precision (compared to experiment), with the precision depending upon how much mathematical work is put into the analysis.<ref>Pierre Ramond. <i>Field Theory: A Modern Primer</i>, Chapter VIII; Benjamin-Cummings Inc. (1981)</ref>