On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields. II: Case of Interacting Electromagnetic and Electron Fields

Koba, Z.; Tati, Takao; Tomonaga, Sin-itirô

doi:10.1143/ptp/2.3.101

Cited by 50 publications

(20 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2, we show the result of the numerical computation of the principal value part shown in Eq. (9) and show that the real part of the first Meijer-G-approximants coincides with the exact numerical values with good accuracy. This is in agreement with the conjecture in Ref [36].…”

Section: Resummation Of the Renormalons In The φ 4 Modelsupporting

confidence: 56%

“…Since the early days of the Quantum Field Theory (QFT) the problem of the infinities, appearing in the calculations of physical quantities and making the theory apparently inconsistent, was noted by Pauli and Heisenberg [1]. Fortunately, there is the well known procedure of renormalization that improve the convergence [2][3][4][5][6][7][8][9][10]. As a by product, the perturbative renormalization prescriptions [11] appear for processes that can be described using small coupling constants.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-local Lagrangians from renormalons and analyzable functions

Maiezza

Vásquez

2019

Annals of Physics

View full text Add to dashboard Cite

We embed in a generalized Borel procedure the notion of renormalization and renormalons. While there are several efforts in literature to have a semi-classical understanding of the renormalons, here we argue that this is not the fundamental issue and show how to deal with the problem. We find that the effective Lagrangians describing the effects of renormalons are non-local in space but local in time. The quark-antiquark potential in QCD with an infinite number of fermions is also analyzed. The connection between the analyzable functions, the Callan-Symanzyk equation and the renormalons, provides an insight of a non-perturbative renormalization from the standard perturbative renormalization approach.

show abstract

Section: Resummation Of the Renormalons In The φ 4 Modelsupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Non-local Lagrangians from renormalons and analyzable functions

Maiezza

Vásquez

2019

Annals of Physics

View full text Add to dashboard Cite

show abstract

“…This allows to extract an experimental value for the g-factor for the elements for which the transition probability between hyperfine levels has been measured, like 209 Bi 82+ . In this case one finds 49.5(65) ms [452] leading to g (e) =1.78 (12). It would require an improvement of the transition probability by two orders of magnitude to be sensitive to the QED corrections through (47).…”

Section: Landé G-factorsmentioning

confidence: 99%

QED tests with highly charged ions

Indelicato

2019

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

View full text Add to dashboard Cite

The current status of bound state quantum electrodynamics calculations of transition energies for few-electron ions is reviewed. Evaluation of one and two body QED correction is presented, as well as methods to evaluate many-body effects that cannot be evaluated with present-day QED calculations. Experimental methods, their evolution over time, as well as progress in accuracy are presented. A detailed, quantitative, comparison between theory and experiment is presented for transition energies in few-electron ions. In particular the impact of the nuclear size correction on the quality of QED tests as a function of the atomic number is discussed. The cases of hyperfine transition energies and of bound-electron Landé g-factor are also considered.

show abstract

“…In the Tomonaga-Schwinger approach [28,12,13,25], one attributes a vectorψ Σ in a fixed Hilbert spaceH to every spacelike hypersurface Σ ⊂ R 4 . (Throughout this paper, we simply say "spacelike hypersurface" for "spacelike Cauchy hypersurface.")…”

Section: Overviewmentioning

confidence: 99%

“…if Φ is a fermionic field, with the understanding that x k is the coordinate of the k-th anti-particle, just as x j is that of the j-th particle, and that Φ(x) = a(x) + b † (x), with a the particle annihilator and b the anti-particle annihilator. Note that Equations (11) and (12) form natural generalizations of the following relation that always holds between a vector |ψ in (bosonic or fermionic) Fock space and its particle-position representation on collision-free configurations:…”

Section: Overviewmentioning

confidence: 99%

Multi-time wave functions for quantum field theory

Petrat¹,

Tumulka²

2014

Annals of Physics

138

View full text Add to dashboard Cite

Multi-time wave functions such as φ(t 1 , x 1 , . . . , t N , x N ) have one time variable t j for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t, x 1 , . . . , x N ) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multitime wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle-position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga-Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space-time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages.Key words: Tomonaga-Schwinger equation; many-time formalism; particleposition representation of quantum states; consistency of multi-time Schrödinger equations; relativistic wave functions; wave functions on spacelike hypersurfaces; operator-valued fields; Heisenberg picture in quantum field theory.

show abstract

On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields. II: Case of Interacting Electromagnetic and Electron Fields

Cited by 50 publications

References 1 publication

Non-local Lagrangians from renormalons and analyzable functions

Non-local Lagrangians from renormalons and analyzable functions

QED tests with highly charged ions

Multi-time wave functions for quantum field theory

Contact Info

Product

Resources

About