Nonuniqueness of gravity induced fermion interaction in the Einstein-Cartan theory

Kaźmierczak, Marcin

doi:10.1103/physrevd.78.124025

Cited by 6 publications

(12 citation statements)

References 28 publications

(41 reference statements)

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“…where J µ (V ) = ψγ µ ψ and J µ (A) = ψγ µ γ 5 ψ are the Dirac vector and axial currents. A shown in [3] and [3], drastically different prediction of both EC and Holst-modified EC theory can be obtained by changing the parameters a and b of (III.1) if MCP is used.…”

Section: The Ambiguity Of Mcp In the Presence Of Torsionmentioning

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: The Ambiguity Of Mcp In the Presence Of Torsionmentioning

confidence: 99%

“…as a gauge field part of the Lagrangian, since the Holst term is also invariant under the local Poincaré transformations. 3 The parameter β representing the relative weight of the two terms is called the Immirzi parameter.…”

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confidence: 99%

The Poincaré Gauge Theory of Gravity and the Immirzi Parameter

Kaźmierczak

2012

The Twelfth Marcel Grossmann Meeting

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“…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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“…Although this problem was observed already by Kibble [3], it has been largely ignored in the subsequent investigations concerning EC theory. The resulting ambiguity can be physically important for the standard Einstein-Cartan theory and its modifications [4,5]. It seems that MCP should be somehow modified for the sake of connections with torsion, so that it gives equivalent results for equivalent flat space Lagrangians.…”

Section: Introductionmentioning

confidence: 99%

Modified coupling procedure for the Poincaré gauge theory of gravity

Kaźmierczak

2009

Phys. Rev. D

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The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincaré gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique.

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Nonuniqueness of gravity induced fermion interaction in the Einstein-Cartan theory

Cited by 6 publications

References 28 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

Modified coupling procedure for the Poincaré gauge theory of gravity

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