TY - JOUR
T1 - Spacelike charges, null-plane charges, and mass splitting
AU - Gal-Ezer, Eldad
AU - Horwitz, Lawrence P.
PY - 1976
Y1 - 1976
N2 - The properties of charges defined as integrals over tensor densities and their possible use in the treatment of broken symmetries are studied. It is well known that spacelike integrals over nonconserved densities cannot yield charge operators at a fixed sharp time. However, charge operators which are smeared in time with suitable "adiabatic" functions, when there is a mass gap, are well defined; these charges can give rise to a finite algebraic structure only in the infinite-momentum limit, corresponding to an algebra of null-plane charges. For the study of null-plane charges, tensor densities are divided into four classes (very good, good, bad, very bad) according to their transformation properties under the Lorentz group. We argue that in the absence of massless particles members of the first two classes are expected to yield well-defined null-plane charges, while members of the last two classes are not expected to define null-plane charges. The existence of null-plane charges for good densities depends on whether the Pomeron intercept αP(0) is less than 1 or equal to 1. Null-plane Fourier transforms (which appear in the discussion of current algebra at infinite momentum) are also considered. Null-plane charges may satisfy algebraic relations which involve the Poincaré algebra. Owing to domain properties, only semialgebraic relations, which are a generalization of the usual Lie algebraic relations, can be postulated on particle states. Using these relations, a no-go theorem of the O'Raifeartaigh type, which applies to the null-plane charges, is formulated and proved.
AB - The properties of charges defined as integrals over tensor densities and their possible use in the treatment of broken symmetries are studied. It is well known that spacelike integrals over nonconserved densities cannot yield charge operators at a fixed sharp time. However, charge operators which are smeared in time with suitable "adiabatic" functions, when there is a mass gap, are well defined; these charges can give rise to a finite algebraic structure only in the infinite-momentum limit, corresponding to an algebra of null-plane charges. For the study of null-plane charges, tensor densities are divided into four classes (very good, good, bad, very bad) according to their transformation properties under the Lorentz group. We argue that in the absence of massless particles members of the first two classes are expected to yield well-defined null-plane charges, while members of the last two classes are not expected to define null-plane charges. The existence of null-plane charges for good densities depends on whether the Pomeron intercept αP(0) is less than 1 or equal to 1. Null-plane Fourier transforms (which appear in the discussion of current algebra at infinite momentum) are also considered. Null-plane charges may satisfy algebraic relations which involve the Poincaré algebra. Owing to domain properties, only semialgebraic relations, which are a generalization of the usual Lie algebraic relations, can be postulated on particle states. Using these relations, a no-go theorem of the O'Raifeartaigh type, which applies to the null-plane charges, is formulated and proved.
UR - http://www.scopus.com/inward/record.url?scp=35949039145&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.13.2413
DO - 10.1103/PhysRevD.13.2413
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AN - SCOPUS:35949039145
SN - 0556-2821
VL - 13
SP - 2413
EP - 2436
JO - Physical Review D
JF - Physical Review D
IS - 8
ER -