Equal-time relativistic two-body equations

Malvetti, M.; Pilkuhn, H.

doi:10.1016/0370-1573(94)90115-5

Cited by 13 publications

(15 citation statements)

References 112 publications

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“…The index k assumes the four values k = s = (f, 0) (singlet), k = 1 = (f, 1) (triplet with orbital angular momentum l = f ) and k = + , k = − (triplets with l = f and eigenvalues ∓1 of σ 1r σ 2r = σ 1 rσ 2 r) [8]. We arrange the radial wave functions as follows:…”

Section: Solving the New Equation Nonperturbativelymentioning

confidence: 99%

“…An analytic solution of the equations is obtained when the hyperfine operator is replaced by an equivalent r −2 -operator. At this level of precision, the equation becomes equivalent to the one derived from the Dirac-Breit equation [8,9], where the replacement was achieved by the substitution r = r ′ − Zαa/2µ (see section 8 for a).…”

Section: Solving the New Equation Nonperturbativelymentioning

confidence: 99%

“…It exploits the fact that the chirality operator γ 5 1 γ 5 2 commutes with the matrix γ 0 1 γ 0 2 of the parity transformation; a corresponding separation of components does not exist for a single Dirac particle. We begin with the rederivation of an eight-component equation for two free spin-1/2 particles, in which the spin operator of particle 2 is removed in the cms (p 1 = −p 2 = p) [7][8][9], by means of a new matrix c, given in (20) below. The spin dependence in the lab system is generated by a boost, to be discussed in section 5.…”

Section: Introductionmentioning

confidence: 99%

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Eight-component two-fermion equations

Häckl¹,

Hund²,

Pilkuhn³

1998

Phys. Rev. A

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An eight-component formalism is proposed for the relativistic two-fermion problem. In QED, it extends the applicability of the Dirac equation with hyperfine interaction to the positronium case. The use of exact relativistic two-body kinematics entails a CP-invariant spectrum which is symmetric in the total cms energy. It allows the extension of recent \alpha^6 recoil corrections to the positronium case, and implies new recoil corrections to the fine and hyperfine structures and to the Bethe logarithm.Comment: Revtex, accepted for publication in Phys. Rev.

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Section: Solving the New Equation Nonperturbativelymentioning

confidence: 99%

Section: Solving the New Equation Nonperturbativelymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eight-component two-fermion equations

Häckl¹,

Hund²,

Pilkuhn³

1998

Phys. Rev. A

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“…The reason is that the Zeeman operator must be an odd function of E. In fact, any small change δE caused by CPT -invariant perturbations must be odd in E. In the case at hand, CPT -invariance requires equal energy levels for muonium and antimuonium, even in the presence of a magnetic field. Both systems are described by a single eigenvalue equation, with E 2 as eigenvalue (Malvetti and Pilkuhn 1994). First-order perturbation theory produces a small shift δ(E 2 ), from which δE follows as in eq.…”

Section: Dirac Hyperfine Splittingmentioning

confidence: 99%

calCcalPcalT-invariant two-fermion Dirac equation with extended hyperfine operator

Hund

Pilkuhn

2000

J. Phys. B: At. Mol. Opt. Phys.

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For the S-states of muonium and positronium, the hyperfine shifts to the order α 6 of a recently derived two-fermion equation with explicit CPT -invariance are checked against the results of a nonrelativistic reduction, and the leading α 8 shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for r → 0 of the Dirac hyperfine operator, such that the resulting extended operator can be used nonperturbatively. The binding correction to magnetic moments is mentioned.

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“…There is a substantial literature on two-body equations (and also for more complicated systems) in relativistic quantum mechanics as well as quantum field theory, as discussed in [5], [6], [7], [8], and [4].…”

Section: Introductionmentioning

confidence: 99%

Kinematic mass of a composite in the many-particle Dirac model

Hagelstein¹,

Chaudhary²

2012

Preprint

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We are interested in the energy-momentum relation for a moving composite in relativistic quantum mechanics in many-particle Dirac models. For a manifestly covariant model one can apply the Lorentz transform to go from the rest frame to a moving frame to establish an energy-momentum relation of the form (M * c 2 ) 2 + c 2 |P| 2 where M * is the kinematic mass. However, the many-particle Dirac model is not manifestly covariant, and some other approach is required. We have found a simple approach that allows for a separation of relative and center of mass contributions to the energy. We are able to define the associated kinematic energy and determine the energy-momentum relation. Our result can be expressed as a modified deBroglie relation of the formwhere the kinematic mass M * will depend on the total momentum P for a general noncovariant potential. The prefactor that occurs we associate with a time dilation effect, the existence of which has been discussed previously in the literature.

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Equal-time relativistic two-body equations

Cited by 13 publications

References 112 publications

Eight-component two-fermion equations

Eight-component two-fermion equations

calCcalPcalT-invariant two-fermion Dirac equation with extended hyperfine operator

Kinematic mass of a composite in the many-particle Dirac model

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