Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action

S\"oren Holst (Department of Physics; Stockholm University)

REVIEW

Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action

Sören Holst (Department of Physics, Stockholm University)

General Relativity and Quantum Cosmology · Submitted 7 Nov 1995 · 5 references

Pith's verdict: A short, correct paper that quietly introduced the one-parameter action underlying real-variable LQG; the derivation is sound, with one compressed step and one honestly flagged on-shell argument.

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arXiv IDgr-qc/9511026 (version 1)

Pith IDP5QFMK75, Pith's permanent record of this paper and its review

CitationS\"oren Holst (Department of Physics, Stockholm University). "Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action." arXiv:gr-qc/9511026 (1995). https://pith.science/paper/P5QFMK75

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Editor's note

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This is the paper that put the Holst action on the map, and it deserves the reputation it has. The new content is Eq. (1): the Hilbert-Palatini action with a curvature-dual term weighted by a free parameter alpha. The author shows by explicit 3+1 decomposition that alpha = 0 gives ADM, alpha = i gives Ashtekar's self-dual formulation, and alpha = 1 gives Barbero's real connection Hamiltonian, with the identification alpha = beta^{-1} in Eq. (14). Barbero had the Hamiltonian but no Lagrangian; Samuel and Jacobson-Smolin had only the self-dual case. Getting all three from one action principle is a real result, and it is done with standard, checkable algebra rather than hand-waving at the level of the setup. The comparison to Barbero's published constraint is an independent cross-check, and it lands. That is the strongest thing you can say about a derivation like this, and it holds here. Two soft spots, both minor. First, the equivalence-to-GR argument in Eq. (4) is on-shell: it uses A = Levi-Civita from the A-equation of motion, and the author says so plainly ('this only is true when the evolution equations is used') and hedges that the term 'should be' a total derivative. That hedge is honest but unproved, and it is the one place where a reader has to take something on faith. Second, the step from the three primary constraints to Eq. (12) is compressed into 'a lengthy manipulation.' That is the load-bearing step, and it is not reproducible from the text alone. Neither is a correctness problem; both are presentation gaps that the later literature filled in. One scope note, not a flaw: the paper never says what alpha means physically. That turned out to be the Barbero-Immirzi parameter, and the paper is not obliged to know that. Who should read it: anyone working on canonical gravity or on the covariant starting point for LQG, and anyone who wants to see how a parameter in an action propagates into a constraint algebra. It is short enough to read in an afternoon and it rewards the read. This deserves a serious referee, though the referee's job is mostly to ask for the Eq. (12) algebra to be shown rather than to question the result.

Referee report

Major objections (3)

[Eq. (4) and the paragraph following it] The argument that the added dual term does not change the physical content rewrites it as ε^{αβγδ}R_{αβγδ} and sets it to zero 'since R^δ_{[αβγ]} = 0.' This uses Eq. (3), A = Levi-Civita, i.e., the connection equation of motion, so the equivalence to general relativity is established only on-shell; the manuscript acknowledges this ('this only is true when the evolution equations is used') and hedges that the term 'should be' a total derivative. Because the central claim is that (1) defines GR for all complex α, the off-shell statement should be supplied: for instance, show that the connection equation forces vanishing torsion, after which the dual term vanishes identically and the tetrad equation reduces to Einstein's. As written, the 'should be' is an assertion rather than a result.
[The passage from the three constraints following Eq. (9) to Eq. (12)] The step that solves for +A_{ai} and yields Eq. (12), +A = -A − 2αΓ, is compressed into 'A lengthy manipulation of these yields.' This is the load-bearing step of the paper: it is where the second-class constraint is solved and the action is reduced to Barbero's form, and it cannot be checked from the text without independent recomputation. An appendix giving the intermediate contractions, or at least the key identities used to eliminate A_t^{i0} and A_t^{ij}, would make the central derivation verifiable.
[The paragraph identifying the four terms of Eq. (13) with Barbero's formulation] The identification is asserted ('we recognize the four terms in (13) as ... in Barbero's formulation (where the scalar constraint is of the form in formula (18) in [4])') rather than shown term by term. Since the central claim is that (13) is Barbero's Hamiltonian, an explicit match — inserting the dictionary (14), α = β^{-1} and -A = α BarA, and displaying the resulting Gauss, vector, and scalar constraints against Barbero's (18) — would make the claim checkable and would expose any sign or factor convention differences.

Minor objections (7)

[After Eq. (9)] The line 'ǫijk ≡ ǫ0ijk and ǫijk ≡ −ǫ0ijk' defines the same symbol twice with opposite signs; presumably one is ǫ_{ijk} and the other ǫ^{ijk}, and the text should distinguish raised and lowered indices explicitly.
[Eq. (5)] The transformation law as printed is garbled ('{A^a_i → A'^a_i + γ δf[E]/δE^a_i, E^a_i → E'^a_i = E^a_i}'); the role of γ and the precise form of the shift should be written cleanly.
[Eq. (12) and the sentence 'Hence (12) should be inserted into the action'] The justification that (12) is second class rests on the 'naive canonical Poisson Brackets' and the bracket {+A − -A + 2αΓ, +Ψ} = 1. Since Γ = Γ[E] depends on E, the bracket should be stated at fixed E, and the legitimacy of substituting a second-class constraint into the action (rather than passing to Dirac brackets) deserves one or two explicit lines.
[Abstract and the paragraph introducing α] The abstract emphasizes that Barbero's formulation is real, but the text introduces α as a '(complex) parameter' without stating for which α the resulting variables are real (real α = β^{-1}) and for which they are complex (α = i). A sentence making this explicit would align the body with the abstract.
[Second paragraph] The sentence 'Our claim here is that α = 1 leads to Barbero's Hamiltonian with his parameter β = 1' is followed later by α = β^{-1}; the two are consistent, but the earlier phrasing invites the appearance of a mismatch and could be reworded to point forward to (14).
[Eq. (1)] The determinant e and the overall factor 1/2 should be accompanied by an explicit sign/absolute-value convention for the Lorentzian tetrad determinant.
[Throughout] There are several typographical errors: 'phase spase' (first paragraph), 'canditate' (second paragraph), 'diﬀer' (after Eq. 4), 'skift' (after Eq. 9), 'natur ally' (after Eq. 12), 'Futhermore' (after Eq. 13), 'cheer ed' (acknowledgments), and the grammar of 'the evolution equations is used.' These should be corrected.

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The paper

The paper claims

A single one-parameter action, the Hilbert-Palatini integrand with the curvature mixed with its dual, is claimed to generate Barbero's real connection formulation of general relativity, with the ADM and Ashtekar formulations appearing as $α

The reading

General relativity admits several Hamiltonian formulations, and by the mid-1990s the menu included the ADM metric variables, Ashtekar's complex connection variables (which simplify the constraints but require reality conditions to be imposed by hand), and Barbero's real connection variables (which keep the variables real at the cost of a more complicated Hamiltonian constraint). The Hilbert-Palatini action was known to produce ADM, and its self-dual truncation was known to produce Ashtekar; Barbero's version had no action of its own. This paper proposes one: the Hilbert-Palatini integrand with the curvature tensor replaced by a one-parameter mixture of the curvature and its dual. If the claim holds, the three canonical formulations are not rival starting points but three settings of a single dial, and Barbero's real variables come equipped with a Lagrangian. That matters because a Lagrangian is what allows path-integral, covariance, and symmetry arguments to be brought to bear on a canonical scheme.

What carries the argument

The load-bearing device is the one-parameter action built from the tetrad and a curvature mixed with its dual. The dual admixture is what lets the configuration variable stay a real connection while still encoding the spatial Levi-Civita connection plus a fixed multiple of the extrinsic curvature; the mixing angle is exactly what interpolates between the metric-based and the self-dual descriptions. The second device is the elimination of the rotational part of the spin connection using the evolution equations and its substitution back into the action, which converts a first-order tetrad action into a canonical action whose constraints can be read off term by term.

Extended reading notes

Core claim

The paper's claim is that the action $$S = ½∫ e e^α{}_I e^β{}_J ($F^{{IJ}}${}_{αβ} − α *$F^{{IJ}}${}_{αβ})$$ with a (complex) parameter $α$ is the Lagrangian underlying Barbero's formulation when $α = β^{-1}$, where $β$ is Barbero's own parameter. The two familiar cases sit at the ends: $α = 0$ is the ordinary Hilbert-Palatini action, which 3+1 decomposes to ADM, and $α = i$ keeps only the self-dual part of the curvature, which gives Ashtekar. The derivation proceeds by imposing the time gauge, performing a 3+1 split, and then solving the evolution equations for the rotational (spatial) part of the spin connection, finding $A_{aij} = -ε_{ijk}Γ^k{}_a$, and reinserting it into the action. What remains is a sum of four pieces the author identifies as the kinetic term, the Gauss law constraint, the vector constraint, and the scalar constraint in Barbero's form, with dynamical variable $^-A_{ai} = K_{ai} + αΓ_{ai}$ to be compared with Barbero's $Γ_{ai} + βK_{ai}$. The author also checks that the added dual-curvature term equals the totally antisymmetrized Riemann tensor and therefore vanishes by the first Bianchi identity once the connection is the Levi-Civita one, concluding that the modification differs from ADM by at most a canonical transformation.

Load-bearing premise

The claim that the extra dual-curvature term changes nothing physical rests on evaluating it only after the connection has been set equal to the Levi-Civita one and invoking the first Bianchi identity; the stronger statement that it is a total derivative off shell is asserted rather than proved.

Editorial extensions

If this is right

Barbero's real connection formulation acquires a first-order action principle, so Lagrangian and path-integral methods can be applied to it directly rather than only to Ashtekar's complex version.
The ADM, Ashtekar, and Barbero formulations appear as three values of one parameter in a single Lagrangian, so results established in one can in principle be translated into the others.
For real values of the parameter the connection stays real, so the reality conditions that complicate Ashtekar's quantization are absent from that range of the family.
The decomposition shows explicitly that the spatial part of the connection is forced to be the Levi-Civita spin connection, $A_{aij} = -ε_{ijk}Γ^k{}_a$, once the evolution equations are used.
The scalar constraint in the resulting action carries both a curvature term $\tilde{F}^i{}_{bc}$ and a three-curvature term $R^i{}_{bc}$, matching the structure Barbero reported.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the added dual term is a total derivative only after the equations of motion are imposed, the family of actions is not equivalent off shell, which would matter for any path-integral weighting built on it.
Because the parameter labels genuinely different-looking but classically equivalent formulations, computing the same physical quantity at several values of the parameter would be a consistency check on any regularization or quantization scheme applied to one member of the family.
The same trick — adding a dual piece to the curvature to trade complex variables for real ones — should transfer to other gauge theories with a duality structure, such as BF-type or Yang-Mills-type actions, suggesting a general recipe rather than a gravity-specific accident.
If the parameter survives quantization as a genuine label of inequivalent theories rather than a classical redundancy, its value becomes a physical input rather than a bookkeeping choice, which would make the classical equivalence established here only the first half of the story.

Original abstract

Barbero recently suggested a modification of Ashtekar's choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is a connection, has the advantage of being real. In this article we derive Barbero's Hamiltonian formulation from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,930 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.77 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Barbero recently suggested a modification of Ashtekar's choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is a connection, has the advantage of being real. In this article we derive Barbero's Hamiltonian formulation from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Barbero recently suggested a modification of Ashtekar's choice of canonical variables for general relativity.	background 1.00	0.05	0.05	asserted 0.69
s1	Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is a connection, has the advantage of being real.	background 0.99	0.08	0.08	asserted 1.00
s2	In this article we derive Barbero's Hamiltonian formulation from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action.	contribution 0.97	0.95	0.68	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

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S sections
T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (5)

[1]

1 Ashtekar, A. (1986) Phys.Rev.Lett. 57,

View on Pith 1986
[583]

4 Barbero, J.F. (1995) Phys.Rev. D 51,

View on Pith 1995
[1587]

2 Arnowitt, R., Deser, S., Misner, C.W. (1962) in Gravitation: An introduction to Current Research Ed. L Witten (New York, Wiley) 3 Samuel, J. (1987) Pramana-J. Phys 28 L429. Jacobson, T., Smolin, L. (1988) Class.Quantum Grav. 5,

View on Pith 1962
[2244]

Ashtekar, A. (1987) Phys.Rev. D 36,

View on Pith 1987
[5507]

5 Ashtekar, A., Lewandowski, J., Marolf, D., Mour˜ ao, J., Th iemann, T., preprint gr-qc/9504018. 6 Peld´ an, P. (1994)Class.Quantum Grav. 11,

View on Pith Pith review arXiv 1994

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How later papers used it

235 later papers cite it

Evidence: substantial. 235 of the citing papers share no author with it, and 20 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 349 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

4 later papers by other authors are listed below: 2 built on it, 2 used its method or tool and 1 compared its own results with it. 1 of them appears under more than one label.

Builds on it 2 of 6 papers with this label

Generalized this paper's well-known result to configuration spaces containing asymptotically flat solutions.

The gravitational Hamiltonian, first order action, Poincar\'e charges and surface terms (2015) · 1.00 · paraphrased: the licence does not allow quoting
Obtained a new term in its model as a twist-deformation of this paper's Holst term.

Noncommutative gravity with self-dual variables (2018) · 0.86 · paraphrased: the licence does not allow quoting

Uses its method or tool 2 of 5 papers with this label

Followed this paper to partially fix the gauge by imposing the time-gauge.

The gravitational Hamiltonian, first order action, Poincar\'e charges and surface terms (2015) · 0.90 · paraphrased: the licence does not allow quoting
Used the generalization of this paper's Holst action as the action for N=2 pure supergravity.

Entropy of Black Holes in N=2 Supergravity (2009) · 0.90 · paraphrased: the licence does not allow quoting

Compares with it 1 of 9 papers with this label

Took n^0=-1 in the Lorentzian case so that its results coincide with this paper's results.

Canonical analysis of Holst action without second-class constraints (2019) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

198 arXiv papers cite this in 288 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 163 sentences without a confident label

Builds on it 5 papers

The objective of this paper is to continue and amend the work started in [ref] and to extend the results of [ref] for asymptotically flat boundary conditions.

The gravitational Hamiltonian, first order action, Poincar\'e charges and surface terms · Introduction · 0.97
In the present work we consider a special case of such generalized CSG [ref] with a negative cosmological constant and a new parameter which immitates the Barbero Immirzi parameter of 3+1 gravity [ref] ; the possibility of this generalization also was hinted in the pioneering work [ref] .

2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation · Introduction · 0.85
Our model contains a new term, which is obtained as a twist-deformation of the Holst term [ref] .

Noncommutative gravity with self-dual variables · Introduction · 0.86

Uses its method or tool 3 papers

Following [ref] , we now partially fix the gauge by imposing the time-gauge.

The gravitational Hamiltonian, first order action, Poincar\'e charges and surface terms · 3+1 splitting · 0.90
These are a subset of all solutions of the KSEs of the given supergravity theory.] In this paper, we shall use the generalization of the Holst action [ref] as the action for $𝒩=2$ pure supergravity [ref] .

Entropy of Black Holes in N=2 Supergravity · Introduction · 0.90
This is done by adding to the action a term that vanishes on-shell [ref] .

Gravity-Yang-Mills-Higgs unification by enlarging the gauge group · Introduction · 0.80

Compares with it 4 papers

The aim of this section is to rewrite the system of constraints ([ref])–([ref]) in a form that makes comparison with constraints of General Relativity with Holst term, discussed in [ref] .

Hamiltonian analysis of SO(4,1) constrained BF theory · Simplifying the constraints · 1.00
Of course, the final set of constraints we have obtained has exactly the form of the constraints describing gravity in [ref] .

Deformed BF theory as a theory of gravity and supergravity · Canonical analysis · 0.85
This is in direct contrast to the standard approach to covariant canonical gravity [ref] where the rotation and boost parts of connection do not commute.

In Search of Quantum de Sitter Space: Generalizing the Kodama State · The quantum theory in this formalism · 0.98

Cites it as support 1 paper

One of the motivations to look for a representation different than in the ADM approach was the presence of the $E^a$-dependent functional in a denominator in the Hamiltonian constraint both in the case of the gravitational field's and matter fields' contribution — see [ref] .

Relativistic classical theory II. Holonomy-flux representation of gravitational degrees of freedom · Thiemann's regularization of the ADM model in the Ashtekar representation · 0.96

Cites it as background 94 papers

In particular, a formulation for real general relativity expressed as a constrained BF theory that involves the Immirzi parameter [ref] was given in [ref] by Capovilla, Montesinos, Prieto, and Rojas (hereafter CMPR formulation).

Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter · Introduction · 0.85
Holst generalizes the previous results introducing the Ashtekar-Barbero-Immirzi Lagrangian, carried out from the Hilbert-Palatinin action, known as the Holst action [ref] .

Symplectic analysis for the Holst action with Dirac fields · Introduction · 0.83
The Holst action [ref] , which underpins this model, is given by [equation] where $F=A+12[A,A]$ is the curvature of the $𝔰𝔬(1,3)$ connection, $e^α$ is the co-tetrad and $γ$ is the Barbero–Immirzi parameter [ref] .

Evidence for Planck Luminosity Bound in Quantum Gravity · Introduction · 0.92

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

1 Ashtekar, A. (1986) Phys.Rev.Lett. 57,

View on Pith 1986

[2] [583]

4 Barbero, J.F. (1995) Phys.Rev. D 51,

View on Pith 1995

[3] [1587]

2 Arnowitt, R., Deser, S., Misner, C.W. (1962) in Gravitation: An introduction to Current Research Ed. L Witten (New York, Wiley) 3 Samuel, J. (1987) Pramana-J. Phys 28 L429. Jacobson, T., Smolin, L. (1988) Class.Quantum Grav. 5,

View on Pith 1962

[4] [2244]

Ashtekar, A. (1987) Phys.Rev. D 36,

View on Pith 1987

[5] [5507]

5 Ashtekar, A., Lewandowski, J., Marolf, D., Mour˜ ao, J., Th iemann, T., preprint gr-qc/9504018. 6 Peld´ an, P. (1994)Class.Quantum Grav. 11,

View on Pith Pith review arXiv 1994