Hamiltonian formulations of Yang–Mills theory and gauge ambiguity in quantization

2003 ◽  
Vol 81 (3) ◽  
pp. 545-554 ◽  
Author(s):  
P Bracken
Keyword(s):  
Path Integral ◽  
Integral Formulation ◽  
Quantum Level ◽  
Path Integral Formulation ◽  
Yang Mills ◽  
Axial Gauge ◽  
Gauge Fixing ◽  
The Subject ◽  
Gauge Ambiguity

A general formulation of the Hamiltonian in non-Abelian Yang–Mills theory is given. The subject of gauge-fixing ambiguity is investigated. It is shown how this type of degeneracy affects the Faddeev–Popov prescription for the corresponding path-integral formulation at the quantum level. A method for treating this problem is developed. The ideas are implemented by quantizing the theory in the axial gauge. PACS Nos.: 11.10Ef, 11.15-q, 11.15Tk

Mass gap in Yang's theory of gravity

2015 ◽  
Vol 24 (10) ◽  
pp. 1550070
Author(s):  
Eckehard W. Mielke
Keyword(s):  
Quantum Gravity ◽  
Path Integral ◽  
Open Problem ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Yang Mills ◽  
Mass Gap ◽  
Weyl Invariance ◽  
Vacuum Degeneracy ◽  
Double Duality

The quantization of a curvature-squared model of gravity, in the affine form proposed by Yang, is reconsidered in the path integral formulation. Due to its inherent Weyl invariance, sharing this with internal Yang–Mills fields, it or some of its topological generalizations are still a possible route to quantum gravity. Instanton type solutions with double duality properties exhibit a "vacuum degeneracy", i.e. a bifurcation into distinct classical Einsteinian backgrounds. For linearized fields, this conclusively induces a mass gap in the graviton spectrum, a feature which is an open problem in the quantization of internal Yang–Mills fields.

Nambu–Goldstone theorem and spin-statistics theorem

2016 ◽  
Vol 31 (13) ◽  
pp. 1630018
Author(s):  
Kazuo Fujikawa
Keyword(s):  
Field Theory ◽  
Path Integral ◽  
Integral Formulation ◽  
Theoretical Physics ◽  
Path Integral Formulation ◽  
Goldstone Theorem ◽  
Relativistic Systems ◽  
Present Essay ◽  
The Subject ◽  
Short Comment

On December 19–21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu–Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.

Path integral formulation of centroid dynamics for systems obeying Bose–Einstein statistics

2001 ◽  
Vol 115 (10) ◽  
pp. 4484-4495 ◽  
Author(s):  
Nicholas V. Blinov ◽  
Pierre-Nicholas Roy ◽  
Gregory A. Voth
Keyword(s):  
Path Integral ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Bose Einstein

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

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