Feynman Diagrams for the Yang-Mills Field

Фаддеев, Людвиг Дмитриевич; Попов, В. В.

doi:10.1142/9789814340960_0012

Cited by 57 publications

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“…A helpful identity tells us that if Y (Φ, K) is a functional that behaves as a scalar [i.e. such that Y ′ (Φ ′ , K ′ ) = Y (Φ, K)] under the canonical transformation Φ, K → Φ ′ , K ′ , generated by the functional F (Φ, K ′ ), then we have [26,22] 1) whereF ζ (Φ, K) = F ζ (Φ, K ′ (Φ, K)) and F ζ (Φ, K ′ ) = ∂F/∂ζ. In this formula, the ζ derivative of each functional is evaluated while the natural arguments of the functional are kept constant.…”

Section: Appendix Useful Formulasmentioning

confidence: 99%

“…to fix the gauge in a local way, consist of extending the set of the physical fields φ to a larger set Φ α , which includes the Faddeev-Popov ghosts C [1], the antighostsC and suitable Lagrange multipliers B for the gauge fixing. Moreover, to keep track of the effects of renormalization on the gauge symmetries, external sources K α are coupled to the transformations of the fields.…”

Section: Introductionmentioning

confidence: 99%

“…We show that the nontrivial sector of the cohomology of renormalization just depends on the physical fields φ and (in the case of functionals of nonvanishing ghost numbers) the ghosts C. Precisely, in general gauge theories whose gauge symmetries possibly include general covariance, local Lorentz symmetry, Abelian gauge symmetries and non-Abelian Yang-Mills symmetries, the solution of the problem (S, X) = 0, where X(Φ, K) is a local functional generated by renormalization, has the form 1) where G and Y (Φ, K) are other local functionals. The key ingredient of the proof is the use of the background field method [18] and the comparison with the usual, nonbackground approach.…”

Section: Introductionmentioning

confidence: 99%

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Background field method and the cohomology of renormalization

Anselmi

2016

Phys. Rev. D

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Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating between the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions of the theorem are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved arguments that are available in the literature.

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Section: Appendix Useful Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Background field method and the cohomology of renormalization

Anselmi

2016

Phys. Rev. D

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“…It is well-known that the BRST invariance is the quantized version of the classical gauge symmetry in the context of quantum Yang-Mills gauge theories [12][13][14]. Actually, the BRST invariance can reproduce all the information of gauge symmetries within the quantized formalism.…”

Section: Extended Brst Transformationsmentioning

confidence: 99%

Axial symmetry, anti-BRST invariance, and modified anomalies

Varshovi

2016

Int. J. Geom. Methods Mod. Phys.

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“…(For surveys and references on various approaches of quantum gravity, see 2. The realization that non-Abelian gauge symmetries require the inclusion of opposite-normed ghost fields to compensate the effect of unphysical polarizations in loop corrections [29,32].3. The development of invariant regularization techniques, the first of which was dimensional regularization [33,34].…”

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confidence: 99%

Quantum gravity: A brief history of ideas and some prospects

Carlip

Chiou

et al. 2017

One Hundred Years of General Relativity

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We present a bird's-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity, and black hole thermodynamics.The early ideas at the dawn of quantum gravity as well as the possible observations of quantum gravitational effects in the foreseeable future are also briefly discussed.PACS numbers: 04.60.-m * This article is to be published in International Journal of Modern Physics D and also in the book "One HundredYears of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity," edited by Wei-Tou Ni (World Scientific, Singapore, 2015 Quantum gravity is the research that seeks a consistent unification of the two foundational pillars of modern physics -quantum theory and Einstein's theory of general relativity. It is commonly considered as the paramount open problem of theoretical physics, and many fundamental issues -such as the microscopic structure of space and time, the origin of the universe, the resolution to spacetime singularities, etc. -relies on a better understanding of quantum gravity.The quest for a satisfactory quantum description of gravity began very early. Einstein after proposing general relativity thought that quantum effects must modify general relativity in his first paper on gravitational waves in 1916 [1] (although he switched to a different point of view working on the unification of electromagnetism and gravitation in the 1930s). Klein argued that the quantum theory must ultimately modify the role of spatio-temporal concepts in fundamental physics [2][3][4] and his ideas were developed by Deser [5]. With the interests and developments of Rosenfeld, Pauli, Blokhintsev, Heisenberg, Gal'perin, Bronstein, Frenkel, van Dantzig, Solomon, Fierz, and many other researchers, three approaches to quantum gravity after World War II had already been enunciated in 1930s pre-World War II as summarized by Stachel [6]:1. Quantum gravity should be formulated by analogy with quantum electrodynamics (Rosenfeld, Pauli, Fierz).2. The unique features of gravitation will require special treatment -the full theory with its nonlinear field equations must be quantized and generalized as to be applicable in the absence of a background metric (Bronstein, Solomon).3. General relativity is essentially a macroscopic theory, e.g. a sort of thermodynamics limit of a deeper, underlying theory of interactions between particles (Frenkel, van Dantzig).Many ideas of the early time continue to provide valuable insight about the nature of quantum gravity even today. For example, the 1939 work on linearized general relativity as spin-2 field by Fierz and Pauli [7] inspired a recent development on massive gravity, bimetric gravity, etc.Modern work on quantum gravity, however, did not really start off until the development of a canonical formalism in 1959-1961 by Arnowitt, Deser, and Misner (ADM) for the case of asymptotically flat boundary conditions [8][9][10][11][12][13][14][1...

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Feynman Diagrams for the Yang-Mills Field

Cited by 57 publications

References 0 publications

Background field method and the cohomology of renormalization

Background field method and the cohomology of renormalization

Axial symmetry, anti-BRST invariance, and modified anomalies

Quantum gravity: A brief history of ideas and some prospects

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