About: Two-body Dirac equations

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In quantum field theory, and in the significant subfields of quantum electrodynamics (QED) and quantum chromodynamics (QCD), the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi, the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These "ghost" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from

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rdfs:label	Two-body Dirac equations (en)
rdfs:comment	In quantum field theory, and in the significant subfields of quantum electrodynamics (QED) and quantum chromodynamics (QCD), the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi, the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These "ghost" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from (en)
dcterms:subject	Quantum field theory Equations of physics Dirac equation Mathematical physics
Wikipage page ID	36054202 (xsd:integer)
Wikipage revision ID	1117741601 (xsd:integer)
Link from a Wikipage to another Wikipage	Canonical coordinates Quantum electrodynamics Quantum entanglement Quantum field theory Quarkonium Electromagnetic field Electromagnetism Hydrogen Bethe–Salpeter equation Relativistic quantum mechanics Relativistic wave equations Ricci calculus Quantum field theory Commutator Elementary charge Gamma matrices Particle physics Physical Review A Equations of physics 4-vector Breit equation Nucleon Center-of-momentum frame Dirac equation Elliptic equation Quantum chromodynamics Gregory Breit Hamiltonian mechanics Invariant mass Mathematical physics Lagrange multiplier Lagrangian mechanics Dirac equation Poisson bracket Positronium Special relativity Speed of light Spin-1/2 Spin (physics) Spinor Natural units Lorentz covariance Muonium Faddeev–Popov ghost Dirac equation in the algebra of physical space Metric (mathematics) Manifestly covariant Kinetic momentum Hamiltonian dynamics SI units Electromagnetic interaction Poisson brackets Many body problem 4-gradient 4-momentum 4-potential dbr:Legendre_Hamiltonian dbr:Lippmann–Schwinger
Link from a Wikipage to an external page	http://th-www.if.uj.edu.pl/acta/vol23/pdf/v23p0043.pdf
sameAs	Two-body Dirac equations Two-body Dirac equations Two-body Dirac equations Two-body Dirac equations
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has abstract	In quantum field theory, and in the significant subfields of quantum electrodynamics (QED) and quantum chromodynamics (QCD), the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi, the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These "ghost" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from quantum field theory they can also be derived purely in the context of Dirac's constraint dynamics and relativistic mechanics and quantum mechanics. Their structures, unlike the more familiar two-body Dirac equation of Breit, which is a single equation, are that of two simultaneous quantum relativistic wave equations. A single two-body Dirac equation similar to the Breit equation can be derived from the TBDE. Unlike the Breit equation, it is manifestly covariant and free from the types of singularities that prevent a strictly nonperturbative treatment of the Breit equation. In applications of the TBDE to QED, the two particles interact by way of four-vector potentials derived from the field theoretic electromagnetic interactions between the two particles. In applications to QCD, the two particles interact by way of four-vector potentials and Lorentz invariant scalar interactions, derived in part from the field theoretic chromomagnetic interactions between the quarks and in part by phenomenological considerations. As with the Breit equation a sixteen-component spinor Ψ is used. (en)
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page length (characters) of wiki page	50493 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Two-body_Dirac_equations
is Link from a Wikipage to another Wikipage of	Bethe–Salpeter equation Relativistic quantum mechanics Relativistic wave equations Index of physics articles (T) Breit equation Dirac equation in curved spacetime Dirac equation

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