Gauge invariant regularization of Yang-Mills wave functionals

Hatfield, Brian

doi:10.1016/0370-2693(85)90367-3

Cited by 3 publications

(5 citation statements)

References 4 publications

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“…Let us briefly recall the functional Schrödinger representation of Yang-Mills theory in the temporal gauge A a 0 (x) = 0 [19,20,21,22,23,24]. The canonical momenta are given by…”

Section: Canonical Quantization Of Pure Yang-mills Theory a Remindermentioning

confidence: 99%

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Kanatchikov¹

2004

Reports on Mathematical Physics

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Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formulation, and its connection with the functional Schrödinger representation in the temporal gauge are discussed. The mass gap problem is related to a finite dimensional spectral problem for a generalized Clifford-valued magnetic Schrödinger operator which represents the DW Hamiltonian operator.

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“…Let us briefly recall the functional Schrödinger representation of Yang-Mills theory in the temporal gauge A a 0 (x) = 0 [19,20,21,22,23,24]. The canonical momenta are given by…”

Section: Canonical Quantization Of Pure Yang-mills Theory a Remindermentioning

confidence: 99%

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Kanatchikov¹

2004

Reports on Mathematical Physics

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“…The canonical quantization of YM field theory in the functional Schrödinger picture of QFT [1][2][3][4][5][6][7][8][9][10][11][12][13] leads (in the temporal gauge A a 0 (x) = 0) to the description of the corresponding quantum field in terms of the Schrödinger wave functional Ψ([A a i (x)], t) which satisfies the functional derivative Schrödinger equation Precanonical quantization of YM fields proposed in [14,15] leads to the description in terms of the Clifford-algebra-valued wave function Ψ(A a µ , x µ ) which satisfies the partial derivative precanonical Schrödinger equation…”

Section: Introductionmentioning

confidence: 99%

“…and the constraint 4) which is the quantum counterpart of the antisymmetry of the classical YM field strength…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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SchrÖdinger Wave Functional in Quantum Yang–Mills Theory from Precanonical Quantization

Kanatchikov

2018

Reports on Mathematical Physics

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A relation between the precanonical quantization of pure Yang-Mills fields and the standard functional Schrödinger representation in the temporal gauge is discussed. It is shown that the latter can be obtained from the former when the ultraviolet parameter κ introduced in precanonical quantization goes to infinity. In this limiting case, the Schrödinger wave functional can be expressed as the trace of the Volterra product integral of Clifford-algebra-valued precanonical wave functions restricted to a field configuration, and the canonical functional derivative Schrödinger equation together with the quantum Gauß constraint can be derived from the Dirac-like precanonical Schrödinger equation.

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“…Singer, for example, proposed an elegant 'zeta function' regularization scheme [1]. Later Hatfield [16] and quite recently Krug [17] have advanced alternative proposals, equally applicable to quantum gauge theories -the latter, in particular, involving a gauge invariant 'point splitting' technique.…”

Section: If Nowmentioning

confidence: 99%

Orbit space curvature as a source of mass in quantum gauge theory

Moncrief

Marini

Maitra

2019

Annals of Mathematical Sciences and Applications

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It has long been realized that the natural 'orbit space' for non-abelian Yang-Mills dynamics (i.e., the reduced configuration space of gauge equivalence classes of spatial connections) is a positively curved (infinite dimensional) Riemannian manifold. Expanding upon this result I.M. Singer was led to propose that strict positivity of the corresponding Ricci tensor (computable from the rigorously defined curvature tensor through a suitable zeta function regularization procedure) could play a fundamental role in establishing that the associated Schrödinger operator admits a spectral gap.

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Gauge invariant regularization of Yang-Mills wave functionals

Cited by 3 publications

References 4 publications

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

SchrÖdinger Wave Functional in Quantum Yang–Mills Theory from Precanonical Quantization

Orbit space curvature as a source of mass in quantum gauge theory

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