# Interpolating quantum electrodynamics between instant and front forms

## Abstract

The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter δ spanning between the instant form dynamics (IFD) at δ = 0 and the front form dynamics, which is now known as the light-front dynamics (LFD) at δ = π / 4. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom, which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous contribution to the fermion propagator, which is genuinely distinguished from the ordinary equal-time forward and backward propagation of relativistic fermion degrees of freedom. As discussed recently, the helicity of the on-mass-shell fermion spinors in LFD is also distinguished from the ordinary Jacob-Wick helicity in the IFD with respect to whether the helicity depends on the reference frame or not. To exemplify the characteristic difference of the fermion propagator between IFD and LFD, we compute the helicity amplitudes of typical QED processes such as e ^{+} e ^{-} → γγ and eγ → eγ and present the whole landscape ofmore »

- Authors:

- Publication Date:

- Research Org.:
- North Carolina State Univ., Raleigh, NC (United States)

- Sponsoring Org.:
- USDOE; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

- OSTI Identifier:
- 1465904

- Alternate Identifier(s):
- OSTI ID: 1498963

- Grant/Contract Number:
- FG02-03ER41260

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 3; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Ji, Chueng-Ryong, Li, Ziyue, Ma, Bailing, and Suzuki, Alfredo Takashi. Interpolating quantum electrodynamics between instant and front forms. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.036017.
```

```
Ji, Chueng-Ryong, Li, Ziyue, Ma, Bailing, & Suzuki, Alfredo Takashi. Interpolating quantum electrodynamics between instant and front forms. United States. doi:10.1103/PhysRevD.98.036017.
```

```
Ji, Chueng-Ryong, Li, Ziyue, Ma, Bailing, and Suzuki, Alfredo Takashi. Wed .
"Interpolating quantum electrodynamics between instant and front forms". United States. doi:10.1103/PhysRevD.98.036017.
```

```
@article{osti_1465904,
```

title = {Interpolating quantum electrodynamics between instant and front forms},

author = {Ji, Chueng-Ryong and Li, Ziyue and Ma, Bailing and Suzuki, Alfredo Takashi},

abstractNote = {The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter δ spanning between the instant form dynamics (IFD) at δ = 0 and the front form dynamics, which is now known as the light-front dynamics (LFD) at δ = π / 4. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom, which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous contribution to the fermion propagator, which is genuinely distinguished from the ordinary equal-time forward and backward propagation of relativistic fermion degrees of freedom. As discussed recently, the helicity of the on-mass-shell fermion spinors in LFD is also distinguished from the ordinary Jacob-Wick helicity in the IFD with respect to whether the helicity depends on the reference frame or not. To exemplify the characteristic difference of the fermion propagator between IFD and LFD, we compute the helicity amplitudes of typical QED processes such as e + e - → γγ and eγ → eγ and present the whole landscape of the scattering amplitudes in terms of the frame dependence or the scattering angle dependence with respect to the interpolating angle dependence. Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the infinite momentum frame approach and the LFD.},

doi = {10.1103/PhysRevD.98.036017},

journal = {Physical Review D},

number = 3,

volume = 98,

place = {United States},

year = {2018},

month = {8}

}

DOI: 10.1103/PhysRevD.98.036017

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