Projective symmetries and induced electromagnetism in metric-affine gravity

Janssen, Bert; Jiménez-Cano, Alejandro

doi:10.1016/j.physletb.2018.10.032

Cited by 7 publications

(4 citation statements)

References 20 publications

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“…When the one-form above is a gradient, ξ µ = φ ,µ , we obtain the special case of the linear vector distortion transformation (4) with w 2 = 1, w 1 = w 3 = 0. This has precisely the form of the electromagnetic gauge transformation [18,59] (up to the imaginary factor [4]). This suggests a special geometric relevance for this behaviour of the connection under rescalings, and indeed such will be clarified below in II B.…”

Section: A Scale Transformations In the Palatini Formalismmentioning

confidence: 99%

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Scale Transformations in Metric-Affine Geometry

2019

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This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straighforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries. Contents

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Section: A Scale Transformations In the Palatini Formalismmentioning

confidence: 99%

“…[7,[48][49][50][51][52][53][54][55][56], and some recent discussions of projective invariance in metric-affine geometry are found in Refs. [23,26,27,[57][58][59]].…”

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confidence: 99%

Scale Transformations in Metric-Affine Geometry

2019

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“…However as pointed out in [104], such lift is not sensitive to some of the irreducible components of the non-metricity tensor, and one could in principle choose a non-canonical spin connection by adding terms related to non-metricity and/or torsion by hand (see for instance [104,105]). Since we are concerned with minimal coupling, we will consider only the canonical piece of the spin connection, since any extra terms would change the form of (ϒ N R ) ψ μ potentially adding nonminimal interactions.…”

Section: The Minimally Coupled Spin 1/2 Fieldmentioning

confidence: 99%

Minimal coupling in presence of non-metricity and torsion

Delhom

2020

Eur. Phys. J. C

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We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $$\partial \rightarrow \nabla $$∂→∇ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.

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“…However as pointed out in [91], such lift is not sensible to some of the irreducible components of the non-metricity tensor, and one could in principle choose a non-canonical spin connection by adding terms related to non-metricity and/or torsion by hand (see for instance [91,92]). Since we are concerned with minimal coupling, we will consider only the canonical piece of the spin connection, since any extra terms would change the form of (Γ N R ) µ potentially adding non-minimal interactions.…”

Section: Now Let Usmentioning

confidence: 99%

Minimal coupling in presence of non-metricity and torsion

Delhom

2020

Preprint

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We deal with the question of what are and what are not minimal coupling prescriptions in presence of torsion and/or non-metricity, carefully explaining while the naive substitution ∂ → ∇ is not actually a minimal coupling prescritpion. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCP) lead to different dynamics. To that end, we will first write the Euler-Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that, if the correct minimal coupling prescriptions is applied, for spin 0 and 1 fields the results of MCPL and MCP are equivalent, while for spin 1/2 fields there is a difference if one applies the MCP or the MCPL, since the former leads to charge violation. We will also explicitly show how the usual naive substitution ∂ → ∇ is not a minimal coupling prescription for spin 0, 1/2 and 1 fields in presence of torsion and/or non-metricity.1 Here we use Riemannian to imply that the connection is metric-compatible, and non-Riemannian for otherwise. Notice that Mathematicians have another meaning for Riemannian, which is related to the signature of the metric. Our metrics will be assumed to have Lorentzian signature.

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Projective symmetries and induced electromagnetism in metric-affine gravity

Cited by 7 publications

References 20 publications

Scale Transformations in Metric-Affine Geometry

Scale Transformations in Metric-Affine Geometry

Minimal coupling in presence of non-metricity and torsion

Minimal coupling in presence of non-metricity and torsion

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