Orbit Space Curvature as a Source of Mass in Quantum Gauge Theory

Moncrief, Vincent; Marini, Antonella; Maitra, Rachel

doi:10.48550/arxiv.1809.06318

Cited by 1 publication

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“…Furthermore, as we discussed near the end of Section II of Ref. [52], it is quite plausible that strict positivity of the Bakry-Emery Ricci tensor, though seemingly sufficient for the implication of a spectral gap, is not absolutely necessary for this conclusion to hold.…”

Section: Decay Estimates Onmentioning

confidence: 95%

“…The true, normalizable ground state wave functional must necessarily reflect the presence of the potential energy term in the Schrödinger operator. In a recent paper [52] the authors showed how to modify the original Lichnerowicz argument (in a finite dimensional setting) to allow for the occurrence of such a potential energy term and show that a corresponding gap estimate follows therefrom provided that a suitably defined 'Bakry-Emery Ricci tensor' is bounded positively away from zero. This Bakry-Emery Ricci tensor differs from the actual Ricci tensor by a term in the (covariant) Hessian of the logarithm of the true ground state wave function.…”

Section: Decay Estimates Onmentioning

confidence: 99%

“…Though our main focus in Ref. [52] was on the Yang-Mills system we proved therein that (non-vanishing) orbit space curvature also arises naturally through the (minimal) coupling of a Maxwell field to a charged scalar field. In this case curvature arises only for the scalar factor of the (product) orbit space and not for the Maxwell factor which remains flat.…”

Section: Decay Estimates Onmentioning

confidence: 99%

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A Euclidean Signature Semi-Classical Program

Marini¹,

Maitra²,

Moncrief³

2019

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In this article we discuss our ongoing program to extend the scope of certain, welldeveloped microlocal methods for the asymptotic solution of Schrödinger's equation (for suitable 'nonlinear oscillatory' quantum mechanical systems) to the treatment of several physically significant, interacting quantum field theories. Our main focus is on applying these 'Euclidean-signature semi-classical' methods to self-interacting (real) scalar fields of renormalizable type in 2, 3 and 4 spacetime dimensions and to Yang-Mills fields in 3 and 4 spacetime dimensions. A central argument in favor of our program is that the asymptotic methods for Schrödinger operators developed in the microlocal literature are far superior, for the quantum mechanical systems to which they naturally apply, to the conventional WKB methods of the physics literature and that these methods can be modified, by techniques drawn from the calculus of variations and the analysis of elliptic boundary value problems, to apply to certain (bosonic) quantum field theories. Unlike conventional (Rayleigh/ Schrödinger) perturbation theory these methods allow one to avoid the artificial decomposition of an interacting system into an approximating 'unperturbed' system and its perturbation and instead to keep the nonlinearities (and, if present gauge invariances) of an interacting system intact at every level of the analysis.

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Section: Decay Estimates Onmentioning

confidence: 95%

Section: Decay Estimates Onmentioning

confidence: 99%

Section: Decay Estimates Onmentioning

confidence: 99%

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