Title: Comparing light-front quantization with instant-time quantization

Abstract

Here in this paper we compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the restriction to equal times that makes the commutation (or anticommutation) relations appear to be so different. While our results are valid for both bosons and fermions, for fermions there are subtleties associated with tip of the light cone contributions that need to be taken care of. At the level of Feynman diagrams we show for non-vacuum Feynman diagrams that the pole terms in four-dimensional light-front Feynman diagrams reproduce the widely used three-dimensional light-front on-shell Hamiltonian Fock space formulation in which the light-front energy and light-front momentum are on shell. Moreover, we show that the contributions of pole terms in non-vacuum instant-time and non-vacuum light-front Feynman diagrams are equal. However, because of circle at infinitymore » contributions we show that this equivalence of pole terms fails for four-dimensional light-front vacuum tadpole diagrams. Then, and precisely because of these circle at infinity contributions, we show that light-front vacuum tadpole diagrams are not only nonzero, they quite remarkably are actually equal to the pure pole term instant-time vacuum tadpole diagrams. Light-front vacuum diagrams are not correctly describable by the on-shell Hamiltonian formalism, and thus not by the closely related infinite momentum frame prescription either. Thus for the light-front vacuum sector we must use the off-shell Feynman formalism as it contains information that is not accessible in the on-shell Hamiltonian Fock space approach. We show that light-front quantization is intrinsically nonlocal, and that for fermions this nonlocality is present in Ward identities. One can project fermion spinors into so-called good and bad components, and both of these components contribute in Ward identities. Central to our analysis is that the transformation from instant-time coordinates and fields to light-front coordinates and fields is a unitary, spacetime-dependent translation. Consequently, not only are instant-time quantization and light-front quantization equivalent, because of general coordinate invariance they are unitarily equivalent.« less

Authors:

Mannheim, Philip D. ^[1]; Lowdon, Peter  ^[2];

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Brodsky, Stanley J. ^[3]

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+ Show Author Affiliations

1. Univ. of Connecticut, Storrs, CT (United States)
2. Ecole Polytechnique, Palaiseau (France). Inst. Polytechnique de Paris
3. SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)

Publication Date:

Thu Sep 17 00:00:00 EDT 2020

Research Org.:

SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES); French National Research Agency (ANR)

OSTI Identifier:

1768218

Alternate Identifier(s):

OSTI ID: 1874408

Grant/Contract Number:  

AC02-76SF00515

Resource Type:

Accepted Manuscript

Journal Name:

Physics Reports

Additional Journal Information:

Journal Volume: 891; Journal ID: ISSN 0370-1573

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Light-front quantization; Light-front vacuum diagrams