Standard

Gauge-invariant regularization of quantum field theory on the light front. / Paston, S. A.; Prokhvatilov, E. V.; Franke, V. A.

In: Theoretical and Mathematical Physics, Vol. 139, No. 3, 06.2004, p. 807-822.

Research output: Contribution to journal › Article › peer-review

Harvard

Paston, SA, Prokhvatilov, EV & Franke, VA 2004, 'Gauge-invariant regularization of quantum field theory on the light front', Theoretical and Mathematical Physics, vol. 139, no. 3, pp. 807-822. https://doi.org/10.1023/B:TAMP.0000029703.24839.1b

APA

Paston, S. A., Prokhvatilov, E. V., & Franke, V. A. (2004). Gauge-invariant regularization of quantum field theory on the light front. Theoretical and Mathematical Physics, 139(3), 807-822. https://doi.org/10.1023/B:TAMP.0000029703.24839.1b

Vancouver

Paston SA, Prokhvatilov EV, Franke VA. Gauge-invariant regularization of quantum field theory on the light front. Theoretical and Mathematical Physics. 2004 Jun;139(3):807-822. https://doi.org/10.1023/B:TAMP.0000029703.24839.1b

Author

Paston, S. A. ; Prokhvatilov, E. V. ; Franke, V. A. / Gauge-invariant regularization of quantum field theory on the light front. In: Theoretical and Mathematical Physics. 2004 ; Vol. 139, No. 3. pp. 807-822.

BibTeX

@article{290320e388f340e9a0d389d235e75fb8,
title = "Gauge-invariant regularization of quantum field theory on the light front",
abstract = "We briefly describe problems of the Hamiltonian approach for quantizing gauge fields on the light front for space-time bounded by the inequality |x -| ≤ L with periodic boundary conditions in the variable x - imposed on all fields (the DLCQ method). With these restrictions, we consider the gauge-invariant ultraviolet regularization by passing to a lattice in transverse coordinates. We remove the remaining ultraviolet divergences in the longitudinal momentum p_ by imposing a gauge-invariant finite-mode regularization. It turns out that the canonical formalism on the light front with such a regularization imposed does not contain the usual most complicated second-class constraints between zero and nonzero modes of fields. The described scheme can be used both to regularize the standard gauge theory and to provide a gauge-invariant formulation of effective low-energy models on the light front. Because the manifest Lorentz invariance is broken in our formalism, the vacuum state is poorly defined. We discuss this problem, in particular, in relation to the problem of passing to the continuous space limit.",
keywords = "Gauge fields, Hamilton approach, Light front, Transverse lattice",
author = "Paston, {S. A.} and Prokhvatilov, {E. V.} and Franke, {V. A.}",
year = "2004",
month = jun,
doi = "10.1023/B:TAMP.0000029703.24839.1b",
language = "English",
volume = "139",
pages = "807--822",
journal = "Theoretical and Mathematical Physics (Russian Federation)",
issn = "0040-5779",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Gauge-invariant regularization of quantum field theory on the light front

AU - Paston, S. A.

AU - Prokhvatilov, E. V.

AU - Franke, V. A.

PY - 2004/6

Y1 - 2004/6

N2 - We briefly describe problems of the Hamiltonian approach for quantizing gauge fields on the light front for space-time bounded by the inequality |x -| ≤ L with periodic boundary conditions in the variable x - imposed on all fields (the DLCQ method). With these restrictions, we consider the gauge-invariant ultraviolet regularization by passing to a lattice in transverse coordinates. We remove the remaining ultraviolet divergences in the longitudinal momentum p_ by imposing a gauge-invariant finite-mode regularization. It turns out that the canonical formalism on the light front with such a regularization imposed does not contain the usual most complicated second-class constraints between zero and nonzero modes of fields. The described scheme can be used both to regularize the standard gauge theory and to provide a gauge-invariant formulation of effective low-energy models on the light front. Because the manifest Lorentz invariance is broken in our formalism, the vacuum state is poorly defined. We discuss this problem, in particular, in relation to the problem of passing to the continuous space limit.

AB - We briefly describe problems of the Hamiltonian approach for quantizing gauge fields on the light front for space-time bounded by the inequality |x -| ≤ L with periodic boundary conditions in the variable x - imposed on all fields (the DLCQ method). With these restrictions, we consider the gauge-invariant ultraviolet regularization by passing to a lattice in transverse coordinates. We remove the remaining ultraviolet divergences in the longitudinal momentum p_ by imposing a gauge-invariant finite-mode regularization. It turns out that the canonical formalism on the light front with such a regularization imposed does not contain the usual most complicated second-class constraints between zero and nonzero modes of fields. The described scheme can be used both to regularize the standard gauge theory and to provide a gauge-invariant formulation of effective low-energy models on the light front. Because the manifest Lorentz invariance is broken in our formalism, the vacuum state is poorly defined. We discuss this problem, in particular, in relation to the problem of passing to the continuous space limit.

KW - Gauge fields

KW - Hamilton approach

KW - Light front

KW - Transverse lattice

UR - http://www.scopus.com/inward/record.url?scp=3042723946&partnerID=8YFLogxK

U2 - 10.1023/B:TAMP.0000029703.24839.1b

DO - 10.1023/B:TAMP.0000029703.24839.1b

M3 - Article

AN - SCOPUS:3042723946

VL - 139

SP - 807

EP - 822

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -

ID: 9218516