Duffin-Kemmer formulation of gauge theories

Ôkubo, Susumu; Tosa, Yasunari

doi:10.1103/physrevd.20.462

Cited by 26 publications

(23 citation statements)

References 32 publications

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“…The first order formulation of gauge theories has a simple form with cubic interactions only [1]. The renormalization of the first order formalism has been previously studied in the Yang-Mills theory, from various points of view, mainly to one-loop order.…”

Section: Introductionmentioning

confidence: 99%

BRST renormalization of the first order Yang–Mills theory

Frenkel

Taylor

2017

Annals of Physics

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We examine the renormalization of the first order formulation of the Yang-Mills theory, by using the BRST identities. These preserve the gauge invariance of the theory and enable a recursive proof of renormalizability to higher orders in perturbation theory. The renormalisation involves non-linear mixings as well as re-scalings of the fields and sources, which lead to a renormalized action at all orders.

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Section: Introductionmentioning

confidence: 99%

BRST renormalization of the first order Yang–Mills theory

Frenkel

Taylor

2017

Annals of Physics

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“…In order to get the explicit form of the matrices Sim and ßj in a simple manner, one has to make a further assumption. There are two ways to achieve the same result: [2] and therefore between the ßj too, namely (6). (1) and (6) A different common denotation is…”

Section: Invariant Wave Equationsmentioning

confidence: 95%

B₂ Diagrams and Bhabha Equation with Mass Matrix

Jansen

1981

Zeitschrift Für Naturforschung A

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Till now nearly all papers about the Bhabba equation treat equations with a mass term ml. This is merely a matter of mathematical simplicity, because we will see in this work that important physical fields can only be described by a mass term + m 1. The second aim of this publication is to derive a constructive procedure for the calculation of the representations of the Bhabha equa tion and the tensor and spinor field equations, which are equivalent to them. Invariant Wave EquationsBecause a differential equation of any order is being equivalent to a system of first order dif ferential equations the field equation of a free field without subsidary conditions can be written in the form :(1) -ß* + M )ip = 0. The invariance of this equation under infinitesimal Lorentz transformations y)' = (1 + ieSim)rp yields [1]: [Sim, ßj] + ßk (gij Öl -gm] <5?) = 0, [Slm,M ] = 0 (2) (3) (4) (we use the convention: gn = <722 = 933 = -S'oo = -1, Qik = 0 for i = k). The six Sim fulfill [Si mt -+ 9mkSlp + gipSmk -gikSmp -9mpSlk , k, I, m ,p e { 0 ,1 ,2 ,3 } . (5) The Sim can always be choosen in block-diagonal form and then (4) tells us that because of Schur's lemma M is a diagonal matrix. Slm = Sl im Um M = mi m\ mk mkIn order to get the explicit form of the matrices Sim and ßj in a simple manner, one has to make a further assumption. There are two ways to achieve the same result:1) Put ßj = S4], ßi = S41, £744 = -1, 04/ =9j4 = 0, j e { 0,1 ,2 ,3 }. Now(3) has the same structure as (5) and demand ing , $ 4 = -g^Sim = Sim (6) (3), (4), (6) can be written: , = gmk^lp + 9lp®mk ~ gik^mp -gmpSlk, k, I, m ,p e { 0 ,1 ,2 ,3 ,4 } .

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“…It is known that Yang–Mills theory in four dimensions admits an alternative formulation which only makes use of first order rather than second order differential operators and has only cubic interactions. Let M now be a smooth compact four‐dimensional Riemannian manifold without boundary and let

sans-serifG

be a Lie group with Lie algebra

frakturg

with metric

{false⟨ -, - false⟩}_{g}

.…”

Section: Classical L∞‐structure Of Field Theoriesmentioning

confidence: 99%

L_∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

Jurčo

Raspollini

Sämann

et al. 2019

Fortschritte der Physik

221

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We review in detail the Batalin–Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory gives rise to an L∞‐algebra and how quasi‐isomorphisms between L∞‐algebras correspond to classical equivalences of field theories. A few experts may be familiar with parts of our discussion, however, the material is presented from the perspective of a very general notion of a gauge theory. We also make a number of new observations and present some new results. Most importantly, we discuss in great detail higher (categorified) Chern–Simons theories and give some useful shortcuts in usually rather involved computations.

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Duffin-Kemmer formulation of gauge theories

Cited by 26 publications

References 32 publications

BRST renormalization of the first order Yang–Mills theory

BRST renormalization of the first order Yang–Mills theory

B₂ Diagrams and Bhabha Equation with Mass Matrix

L_∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

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Duffin-Kemmer formulation of gauge theories

Cited by 26 publications

References 32 publications

BRST renormalization of the first order Yang–Mills theory

BRST renormalization of the first order Yang–Mills theory

B2 Diagrams and Bhabha Equation with Mass Matrix

L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

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B₂ Diagrams and Bhabha Equation with Mass Matrix

L_∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism