Canonical gravity with fermions

Bojowald, Martin; Das, Rupam

doi:10.1103/physrevd.78.064009

Cited by 90 publications

(161 citation statements)

References 31 publications

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“…In the particular case ̺ = ϑ = 0 the current Y vanishes and there are no second terms, both in the contorsion tensor (11) and in the effective interaction (12). In particular, this ensures that D µ (e e µ I ) = eη IK e µ J C JK µ = 0 and the additional term in the action (1) introducing β coincides with the Nieh-Yan invariant [7].…”

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confidence: 99%

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The Immirzi parameter and fermions with non-minimal coupling

Alexandrov

2008

Class. Quantum Grav.

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We clarify the role played by the Immirzi parameter in classical gravity coupled to fermions. Considering the general non-minimal coupling, we show that, although the torsion depends explicitly on the Immirzi parameter, in a suitable parametrization the effective action obtained by integrating out the spin-connection is independent of it. Thus the Immirzi parameter is not detectable in classical theory even after coupling of fermions.Recently, coupling of fermions to classical general relativity has attracted much attention. The interest was initiated by the work [1] where it has been noted that the minimal coupling to fermions makes gravity sensitive to the so called Immirzi parameter [2]. This parameter, which we call β, appears through the action generalizing the standard Hilbert-Palatini formulation [3]where e I µ is the tetrad field, R IJ µν (ω) is the curvature of the spin-connection ω IJ µ , and the star operator is the Hodge operator defined as ⋆ω IJ µ = 1 2 ε IJ KL ω KL µ . In pure gravity β does not affect the equations of motion. However, in [1] it was demonstrated that once the minimally coupled actionis added and the spin-connection is integrated out, one obtains the following effective 4-fermion interaction term with a β-dependent coupling constantwhere A I = ψγ 5 γ I ψ is the axial current. Thus, it was concluded that measuring the strength of such 4-fermion interaction can provide an information about the Immirzi parameter. In other words, β was argued to be in principle an observable parameter. Later this result was generalized to a non-minimal coupling which was shown to lead to parity violation effects [4,5,6]. *

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confidence: 99%

“…After 1 An attempt to consistently include the minimally coupled fermions in this framework can be found in [11,12]. 2 We use the conventions of [4].…”

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confidence: 99%

The Immirzi parameter and fermions with non-minimal coupling

Alexandrov

2008

Class. Quantum Grav.

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“…We follow the symmetry reduction of torsion-free Bianchi class A models [20,21,22], combined with the canonical formulation of gravity with fermions [14,15,16,23]; the general formulation without symmetry is summarized in the Appendix. Here, we combine these research lines and explore the symmetry reduction of gravity coupled to fermions in a first-order formalism, implying a theory with torsion.…”

Section: Classical Symmetry Reductionmentioning

confidence: 99%

“…It does not have a simple parity behavior and, moreover, it appears in quantized expressions only non-linearly through holonomies. Even in vacuum, this makes a direct demonstration of parity invariance of loop quantum gravity -or the lack thereof -very complicated [16].…”

Section: Introductionmentioning

confidence: 99%

“…If this were to happen, an intriguing new link between particle physics and quantum gravity would result. Seeing whether this is indeed the case requires the introduction of fermions, which is available in loop quantum gravity [14,15,16] (see also [17,18,19]). In general, however, the parity behavior of loop quantum gravity is highly non-trivial due to the fact that the basic variable conjugate to the densitized triad, namely the Ashtekar-Barbero connection, is the sum of a parity-even and a parity-odd term.…”

Section: Introductionmentioning

confidence: 99%

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Fermions in loop quantum cosmology and the role of parity

Bojowald

Das

2008

Class. Quantum Grav.

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Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it is not possible to avoid strong quantum regimes by positing a large matter content. Moreover, possible parity violating effects are important especially in loop quantum cosmology whose basic object is a difference equation for the wave function of the universe defined on a discrete space of triads. The two orientations of a triad are interchanged by a parity transformation, which leaves the difference equation invariant for ordinary matter. Here, we revisit and extend loop quantum cosmology by introducing fermions and the gravitational torsion they imply, which renders the parity issue non-trivial. A treatable locally rotationally symmetric Bianchi model is introduced which clearly shows the role of parity. General wave functions cannot be parity-even or odd, and parity violating effects in matter influence the microscopic big bang transition which replaces the classical singularity in loop quantum cosmology.

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Perturbative Inhomogeneities

Bojowald

2011

Quantum Cosmology

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Canonical gravity with fermions

Cited by 90 publications

References 31 publications

The Immirzi parameter and fermions with non-minimal coupling

The Immirzi parameter and fermions with non-minimal coupling

Fermions in loop quantum cosmology and the role of parity

Perturbative Inhomogeneities

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