Weyl and conformal covariant field theories

Budini, P.; Furlan, P.; Rączka, R.

doi:10.1007/bf02902045

Cited by 20 publications

(16 citation statements)

References 17 publications

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“…On the other hand, Weyl invariance instead does impose constraints on the coupling constants. Our main conclusion is to confirm [14,15,16,22] that Weyl invariance and conformal invariance are independent symmetries: not every Weyl invariant theory is conformal invariant in the weak field limit and conversely, not every conformal invariant theory is Weyl invariant in spite of the fact that it is always invariant under global such Weyl transformations. To illustrate the first part of this statement, let us take for example the following WTDiff invariant theory…”

Section: Discussionmentioning

confidence: 78%

“…We can also look for the most general Lorentz and Weyl invariant lagrangian built with this kind of operators. Again, we need the dimension 4 operator part that will contribute with the Ophq piece of the Weyl variation, which already has two arbitrary constants appearing in it (22). Taking that piece into account, the most general Weyl invariant lagrangian up to dimension 5 operators reads…”

Section: Dimension 5 and Dimension 6 Operators (With 2 Derivatives)mentioning

confidence: 99%

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Conformal invariance versus Weyl invariance

2020

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Section: Discussionmentioning

confidence: 78%

Section: Dimension 5 and Dimension 6 Operators (With 2 Derivatives)mentioning

confidence: 99%

Conformal invariance versus Weyl invariance

2020

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“…With the analysis of the previous section, we know that the dilatation transformation cannot play the role in varying the interaction vertex, since e Thus we choose K μ as a candidate to make γ μ (1 − γ 5 )A μ leave γ μ (1 − γ 5 ) and begin to run. It runs to normal interaction vertex γ μ , as shown in (43), which is for massive fermions. Now let's come back to the equation of our model.…”

Section: Generating Fermion Mass Term With the Help Of Conformal Groupmentioning

confidence: 99%

“…[41][42][43][44][45][46][47][48]. To keep the invariance of x 2 1 + x 2 2 + x 2 3 = 0, one defines the matrix…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

Structure Group and Fermion-Mass-Term in General Nonlocality

Han

Wang

2015

Int J Theor Phys

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In our previous work [J. Math. Phys. 49, 033513 (2008)] two problems remain to be resolved. One is that we lack a minimal group to replace GL(4,C), the other is that the Equation of Motion (EoM) for fermion has no mass term. After careful investigation we find these two problems are linked by conformal group, a subgroup of GL(4,C) group. The Weyl group, a subgroup of conformal group, can bring about the running of mass, charge etc. while making it responsible for the transformation of interaction vertex. However, once concerning the generation of the mass term in EoM, we have to resort to the whole conformal group, in which the generators $K_\mu $ play a crucial role in making vacuum vary from space-like (or light-cone-like)to time-like. Physically the starting points are our previous conclusion, $\vec E^2-\vec B^2\neq 0$ for massive bosons, and the two-photon process yielding $e^+ e^-$ pair. Finally we get to the conclusion that the mass term of strong interaction is linearly relevant to (chromo-)magnetic flux as well as angular momentum.Comment: 14 pages, no figure. Int.J.Theor.Phys.54 (2015

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“…where formally we have used Λ ′µ ν to represent the scaling transformation to every coordinate component [57,59], [61][of which eq. (2)] instead of using the usual form e −α [64]. Slightly different from the operator µ d dµ appearing in renormalization group equation, here the operator D has the usual form D = i x ν ∂ ν , being a hermit one.…”

Section: The Physical Relationship Between the Two Representatiomentioning

confidence: 99%

Scaling Transformation for Nonlocal Interactions

Wang

2015

JMP

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In the light of their relationships with renormalization, in this paper we associate the scaling transformation with nonlocal interactions. On one hand, the association leads us to interpret the nonlocality with locally symmetric method. On the other hand, we find that the nonlocal interaction between hadrons could be test ground for scaling transformation if ascribing the running effects in renormalization to scaling transformation. First we derive directly from group theory the operator/coordinate representation and unitary/spinor representation for scaling transformation, then link them together by inquiring a scaling-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. The main feature of this paper is that we discuss both the representations in a sole physical frame. The representations correspond respectively to the spatial freedom and the intrinsic freedom of the same quantum system. And the latter is recognized to contribute to spin angular momentum that in literature has never been considered seriously. The nonlocal interaction Lagrangian turns out to vary under scaling transformation, analogous to running cases in renormalization. And the total Lagrangian becomes scale invariant only under some extreme conditions. The conservation law of this extreme Lagrangian is discussed and a contribution named scalum appears to the spin angular momentum. Finally a mechanism is designed to test the scaling effect on nonlocal interaction.Comment: 17 pages, 3 figure

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Weyl and conformal covariant field theories

Cited by 20 publications

References 17 publications

Conformal invariance versus Weyl invariance

Conformal invariance versus Weyl invariance

Structure Group and Fermion-Mass-Term in General Nonlocality

Scaling Transformation for Nonlocal Interactions

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