On the problem of mass dependence of the two-point function of the real scalar free massive field on the light cone

Ullrich, Peter; Werner, E.

doi:10.1088/0305-4470/39/20/029

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…On the other hand the Lorentz invariance of (71) means that it has no dependence on z − . Furthermore, (71) is not even a distribution on the Schlieder-Seiler functions because the integral behaves like 1 z 2 ⊥ at the origin [9]. The difference in (71) and ( 72) is because the order of the light-front limit and integral matters.…”

Section: Equivalencementioning

confidence: 99%

“…If the vacuum is annihilated by the light-front annihilation operator then (74) can be used to calculate the two-point Wightman function in terms of the restriction to the light front 0|φ(x)φ(y)|0 = 1 8(2π) 9 dx 1 dỹ 1 d kdp dq q + θ(q + )e…”

Section: Extension To the Local Algebramentioning

confidence: 99%

“…The virtue of free fields is that they are well understood. Others [17][4] [9] have used free fields to develop insight into various aspects of this problem. Algebraic methods provide a resolution of the apparent inconsistency discussed above.…”

Section: Introductionmentioning

confidence: 99%

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Light-front vacuum

Herrmann

Polyzou

2015

Phys. Rev. D

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Background: The vacuum in the light-front representation of quantum field theory is trivial while vacuum in the equivalent canonical representation of the same theory is non-trivial. Purpose: Understand the relation between the vacuum in light-front and canonical representations of quantum field theory and the role of zero-modes in this relation. Method: Vacuua are defined as linear functionals on an algebra of field operators. The role of the algebra in the definition of the vacuum is exploited to understand this relation. Results: The vacuum functional can be extended from the light-front Fock algebra to an algebra of local observables. The extension to the algebra of local observables is responsible for the inequivalence. The extension defines a unitary mapping between the physical representation of the local algebra and a sub-algebra of the light-front Fock algebra. Conclusion: There is a unitary mapping from the physical representation of the algebra of local observables to a sub-algebra of the light-front Fock algebra with the free light-front Fock vacuum. The dynamics appears in the mapping and the structure of the sub-algebra. This correspondence provides a formulation of locality and Poincaré invariance on the light-front Fock space.

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Section: Equivalencementioning

confidence: 99%

Section: Extension To the Local Algebramentioning

confidence: 99%

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Light-front vacuum

Herrmann

Polyzou

2015

Phys. Rev. D

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“…) do not have a canonical restriction to {x 0 + x 3 = 0}. This can be seen by considering the wave front set of D (±) (see [19]). Now the following proposition shows that we can retrieve parameter dependence if we consider the relaxation u * instead of u. ))…”

Section: The Tame Restriction Of a Generalized Functionmentioning

confidence: 99%

Uniqueness in the characteristic Cauchy problem of the Klein–Gordon equation and tame restrictions of generalized functions

Ullrich

2006

Math. Z.

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Abstract. We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a "tame" restriction to the characteristic (hyper)surface {x 0 + x n = 0} in (1 + n)-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space S ′ ∂− (R n ) which we have introduced in [16]. Moreover, we show that every element of S ′ ∂− (R n ) appears as the "tame" restriction of a solution of the (homogeneous) Klein-Gordon equation.

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Light-front puzzles

Polyzou

2024

J. Phys. A: Math. Theor.

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Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interactingsystems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These statesare needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand thestructure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space.The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory.This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries.

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On the problem of mass dependence of the two-point function of the real scalar free massive field on the light cone

Cited by 6 publications

References 12 publications

Light-front vacuum

Light-front vacuum

Uniqueness in the characteristic Cauchy problem of the Klein–Gordon equation and tame restrictions of generalized functions

Light-front puzzles

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