Quantum Theory without Electromagnetic Potentials

DeWitt, Bryce S.

doi:10.1103/physrev.125.2189

Cited by 136 publications

(63 citation statements)

References 7 publications

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“…Soon after the paper by DeWitt appeared [48], Belinfante conjectured that a "path" is just a "gauge" [49]. He showed that, by averaging over path-dependent potential over the directions of all straight lines at constant time converging to the point where the potential is to be calculated, one is led to the potential in the Coulomb gauge [49].…”

Section: Critiques On the Idea Of Stückelberg Symmetry And Gauge-mentioning

confidence: 99%

“…In the past, tremendous efforts have been made to figure out these physical components of the gauge field. DeWitt's formulation of the electrodynamics explained before is one typical example [48]. We realized that, especially useful for our purpose is a slightly more sophisticated formulation proposed in the papers by Ivanov, Korchemsky and Radyushkin [65], [66].…”

Section: Gauge-and Path-independence Of the Evolution Matrix Formentioning

confidence: 99%

“…without introducing gauge-dependent potential [48]. However, it was recognized soon that, although the framework is manifestly gauge-invariant by construction it does depend of the choice of path defining the gauge-invariant potential [49] - [52].…”

Section: Critiques On the Idea Of Stückelberg Symmetry And Gauge-mentioning

confidence: 99%

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Are There Infinitely Many Decompositions of the Nucleon Spin?

Wakamatsu

2014

Int. J. Mod. Phys. Conf. Ser.

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We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. It is crucialy important to recognize the fact that the standard gauge fixing procedure is essentially a process of projecting out the physical components of the massless gauge field. A complexity of the nonabelian gauge theory as compared with the abelian case is that a closed expression for the physical component can be given only with use of the non-local Wilson line, which is generally path-dependent. It is known that, by choosing an infinitely long straight-line path in space and time, the direction of which is characterized by a constant 4-vector n µ , one can cover a class of gauge called the general axial gauge, containing three popular gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within this general axial gauge, we have calculated the 1-loop evolution matrix for the quark and gluon longitudinal spins in the nucleon. We found that the final answer is exactly the same independently of the choices of n µ , which amounts to proving the gauge-independence and path-independence simultaneously, although within a restricted class of gauges and paths.By drawing on all of these findings together with well-established knowledge from gauge theories, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.

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Section: Critiques On the Idea Of Stückelberg Symmetry And Gauge-mentioning

confidence: 99%

Section: Gauge-and Path-independence Of the Evolution Matrix Formentioning

confidence: 99%

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Are There Infinitely Many Decompositions of the Nucleon Spin?

Wakamatsu

2014

Int. J. Mod. Phys. Conf. Ser.

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“…Dirac's ideas lead naturally to consideration of a quantum mechanics in which the wave function has a nonintegrable (or path-dependent) phase factor. This formalism has been developed by various authors (see, for example [23,24,25,26,27,28,29,30,31] and references therein). In general, the path-depndent wave function can be written as…”

Section: Nonassociative Gauge Transformationsmentioning

confidence: 99%

Three-cocycles, nonassociative gauge transformations and Dirac's monopole

Nesterov

2004

Physics Letters A

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“…The awareness about its makeshift status was much stronger in the past than it is now. There were several valiant attempts to avoid the use of indefinite metric by Mandelstam [7] and also DeWitt [8]; their failure also revealed that a description which is consistent with positivity ("off-shell unitarity") requires major new conceptual investments beyond what was known at that time.…”

Section: Introductionmentioning

confidence: 99%

Peculiarities of massive vector mesons and their zero mass limits

Schroer

2015

Eur. Phys. J. C

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Massive QED, in contrast with its massless counterpart, possesses two conserved charges; one is a screened (vanishing) Maxwell charge which is directly associated with the massive vector mesons through the identically conserved Maxwell current, while the presence of a particle-antiparticle counting charge depends on the matter. A somewhat peculiar situation arises for couplings of Hermitian matter fields to massive vector potentials; in that case the only current is the screened Maxwell current and the coupling disappears in the massless limit. In the case of self-interacting massive vector mesons the situation becomes even more peculiar in that the usually renormalizability guaranteeing validity of the first order power-counting criterion breaks down in second order and requires the compensatory presence of additional Hermitian H-fields. Some aspect of these observation have already been noticed in the BRST gauge theoretic formulation, but here we use a new setting based on string-local vector mesons which is required by Hilbert space positivity ("off-shell unitarity"). This new formulation explains why spontaneous symmetry breaking cannot occur in the presence of higher spin s ≥ 1 fields. The coupling to H -fields induces Mexican hat-like self-interactions; they are not imposed and bear no relation with spontaneous symmetry breaking; they are rather consequences of the foundational causal localization properties realized in a Hilbert space setting. In the case of self-interacting massive vector mesons their presence is required in order to maintain the first order power-counting restriction of renormalizability also in second order. The presentation of the new Hilbert space setting for vector mesons which replaces gauge theory and extends on-shell unitarity to its off-shell counterpart is the main motivation for this work. The new Hilbert space setting also shows that the second order Lie-algebra structure of self-interacting vector mesons is a consequence of the principles of QFT and promises a deeper understanding of the origin of confinement. a

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Quantum Theory without Electromagnetic Potentials

Cited by 136 publications

References 7 publications

Are There Infinitely Many Decompositions of the Nucleon Spin?

Are There Infinitely Many Decompositions of the Nucleon Spin?

Three-cocycles, nonassociative gauge transformations and Dirac's monopole

Peculiarities of massive vector mesons and their zero mass limits

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