Modified coupling procedure for the Poincaré gauge theory of gravity

Kaźmierczak, Marcin

doi:10.1103/physrevd.79.127501

Cited by 5 publications

(8 citation statements)

References 26 publications

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“…The transformation formula (IV.2) alone suffices to guarantee local invariance of the final action. If there exists a natural ρ-invariant scalar product structure on Lin(V), which is usually the case [8], then A can be decomposed as…”

Section: Removing the Ambiguity By Modifying The Coupling Proceduresmentioning

confidence: 99%

“…where A is Ran(π)-valued and B(A, e) is Ran(π) ⊥ -valued. Here ⊥ denotes an orthogonal complement (see [8] for the definition of the appropriate scalar product for the Dirac field). Note that B is that part of A that corresponds to the deviation of this procedure from standard YM.…”

Section: Removing the Ambiguity By Modifying The Coupling Proceduresmentioning

confidence: 99%

“…where Dψ := (Dψ) † γ 0 andω a b is an auxiliary connection on space-time, which may differ from ω a b . As shown in [8], the solution of these conditions is provided bỹ…”

Section: Removing the Ambiguity By Modifying The Coupling Proceduresmentioning

confidence: 99%

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The Poincaré Gauge Theory of Gravity and the Immirzi Parameter

Kaźmierczak

2012

The Twelfth Marcel Grossmann Meeting

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The minimal coupling method proved to yield definite and correct physical predictions when applied to fundamental fermions within the framework of Yang-Mills theories of Standard Model. Similarly, the possibility of formulating gravity as the Poincaré gauge theory gives the opportunity to produce definite predictions for fermions in the presence of gravitational field. The minimal coupling procedure, however, cannot be applied naively but rather needs to be modified slightly such that it is unambiguous. Application of the corrected coupling method to fermions, together with the inclusion of the Holst term in the gravitational part of the action, leads to the conclusion that the Immirzi parameter is in principle classically measurable, in agreement with the result of Perez and Rovelli.All the relativistic theories in the absence of gravity are invariant under the (global) action of the Poincaré group. As shown by by Kibble [1], it is possible to obtain a reasonable theory of gravity by simply localizing this global symmetry. This approach necessitates first order formalism for general relativity, with metric (but non-symmetric) connection, as the set of Yang-Mills fields has to consist of ten independent one-forms. Interestingly, this formalism appears to simplify the canonical analysis and quantization of the theory and therefore it is employed in Loop Quantum Gravity (LQG), although in standard LQG the time gauge is imposed at the very beginning that breaks the gauge group effectively to SU (2).The natural way to introduce the interaction within the spirit of Yang-Mills theory is to use the minimal coupling procedure (MCP). Indeed, in the standard model of particle physics this procedure is followed on the fundamental level, leading to predictions that agree with experimental results with great accuracy. Also, in GR the principle of equivalence, which states that the effects of gravitation can be locally 'turned off' by a suitable choice of a reference frame, necessitates minimal coupling [2]. However, in the Poincaré gauge theory of gravity MCP appears to be ambiguous. The ambiguity is of importance for the standard EC theory with fermions [3], as well as the theory modified by the addition of the Holst term [5]. The predictions concerning fermions in the Ashtekar-Barbero-Immirzi formalism obtained in [4] can be radically changed if the freedom of adding divergence of a vector field to the initial fermionic Lagrangian density is exploited [5].Luckily, the corrected unambigoues coupling procedure has been proposed [8] which makes the predictions of the theory unique. They appear to agree with those derived by Perez and Rovelli. II. THE POINCARÉ GAUGE THEORY A. Yang-Mills theoriesThe leading idea of standard Yang-Mills theories is that any interaction can be associated with a symmetry group. LetG be a Lie group and letrepresent the action of a field theory of a matter field φ in Minkowski space M . Here L m is a Lagrangian density and L m a Lagrangian four-form. Assume that V is a (finite dimensional) linear spac...

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Section: Removing the Ambiguity By Modifying The Coupling Proceduresmentioning

confidence: 99%

Section: Removing the Ambiguity By Modifying The Coupling Proceduresmentioning

confidence: 99%

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The Poincaré Gauge Theory of Gravity and the Immirzi Parameter

Kaźmierczak

2012

The Twelfth Marcel Grossmann Meeting

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“…Of course it is possible to view this procedure as a MCP with a modified connection [34]. In any case, the result will be the equivalent action with current-current interaction found in [17].…”

Section: Jcap06(2012)017mentioning

confidence: 99%

“…For the corresponding discussion of the issue related to the BI parameter effects, see, for example, refs. [34][35][36].…”

Section: Jcap06(2012)017mentioning

confidence: 99%

Modified Reset Waveform for High Speed Address under High Ambient Temperature in AC Plasma Display Panel

Jang¹,

Park²,

Tae³

et al. 2011

Jpn. J. Appl. Phys.

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We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w = −1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressure less fluid w = 0 for late universe (corresponding to the limit m → ∞).

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Dirac fields, torsion and Barbero-Immirzi parameter in cosmology

Berredo-Peixoto

Freidel

Shapiro

et al. 2012

J. Cosmol. Astropart. Phys.

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Abstract. We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the BarberoImmirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w = −1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressure less fluid w = 0 for late universe (corresponding to the limit m → ∞).

show abstract

Modified coupling procedure for the Poincaré gauge theory of gravity

Cited by 5 publications

References 26 publications

The Poincaré Gauge Theory of Gravity and the Immirzi Parameter

The Poincaré Gauge Theory of Gravity and the Immirzi Parameter

Modified Reset Waveform for High Speed Address under High Ambient Temperature in AC Plasma Display Panel

Dirac fields, torsion and Barbero-Immirzi parameter in cosmology

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