Gauge invariance and anomalous theories at finite fermionic density

Roberge, André

doi:10.1103/physrevd.41.2605

Cited by 4 publications

(5 citation statements)

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“…It has been noted that the two problems of cosmological genesis -baryo-and magnetogenesis -may be related to each other (Roberge 1989;Field 1994, 1995;Vachaspati 1994). More recently an even stronger reason for a possible connection was proposed (Joyce and Shaposhnikov 1997;Giovannini and Shaposhnikov 1997).…”

Section: Three Topological Forces Acting On a Vortex And Their Analoguesmentioning

confidence: 99%

Vortex formation and dynamics in superfluid 3He and analogies in quantum field theory

Eltsov

Krusius²,

Volovik

2005

Progress in Low Temperature Physics

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The formation and dynamics of topological defects of different structure has been of central interest in the study of the 3 He superfluids. Compared to superfluid 4 He-II, the variability of the important parameters with temperature and pressure is wider and many features are more ideal. This has made experimentally new approaches possible. An example is the formation of quantized vortices and other topological defects in a rapid time-dependent phase transition from the normal state to 3 He-B. This vortex formation process is known as the Kibble-Zurek mechanism and is one the central topics of this review. It demonstrates the use 3 He-B as a model system for quantum fields, with detailed control from the laboratory.PACS: 67.57. Fg, 47.32, 05.70.Fh, 98.80.Cq.

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Section: Three Topological Forces Acting On a Vortex And Their Analoguesmentioning

confidence: 99%

Vortex formation and dynamics in superfluid 3He and analogies in quantum field theory

Eltsov

Krusius²,

Volovik

2005

Progress in Low Temperature Physics

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“…While in 3+1 dimensions these degrees of freedom resist classical treatment, such treatment is possible in one-dimensional models upon bosonization. This approach was first proposed by Roberge [12] who used it to study static properties of sphalerons at a finite fermion density [13]. Here we apply this approach to study the real-time dynamical evolution of the Abelian Higgs model coupled to fermions.…”

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Sphaleron transition rate in the presence of dynamical fermions

1999

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We investigate the effect of dynamical fermions on the sphaleron transition rate at finite temperature for the Abelian Higgs model in one spatial dimension. The fermion degrees of freedom are included through bosonization. Using a numerical simulation, we find that massless fermions do not change the rate within the measurement accuracy. Surprisingly, the exponential dependence of the sphaleron energy on the Yukawa coupling is not borne out by the transition rate, which shows a very weak dependence on the fermion mass.

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“…However, this result indicates that such a naive way of deriving an effective potential at finite density is not correct since, as has been previously found [6,15,16], no local minima of the energy exists when A 1 exceeds 2 √ 2πλc 3 /3e √ 3. Furthermore, this derivation doesn't take into account the fermion back-reaction and the function Φ(z) is not a static solution to the complete set of equations of motion of the original Lagrangian (eq.…”

mentioning

confidence: 74%

“…Fortunately, the situation is simpler in 1+1 dimensional models where one can, through bosonization [13], take into account the fermion back-reaction at the classical level. The present work illustrates some of the non-trivial effects of this fermion back-reaction using a simple model which has been extensively studied in the past, namely the Abelian Higgs model axially coupled to fermions (see for example [6,[14][15][16][17][18]) .…”

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Fermion back reaction and the sphaleron

Roberge¹

1994

Phys. Rev. D

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Using a simple model, a new sphaleron solution which incorporates finite fermionic density effects is obtained. The main result is that the height of the potential barrier (sphaleron energy) decreases as the fermion density increases. This suggests that the rate of sphaleron-induced transitions increases when the fermionic density increases. However the rate increase is not expected to change significantly the predictions from the standard sphaleron-induced baryogenesis scenarios.PACS number(s): 11.15.Kc, 11.1O.KkNonconservation of baryon number in the standard model through quantum effects (anomalies) is well known [I]. While instanton-mediated baryon decays are negligible, the same cannot be said for transitions occurring because of monopole catalysis [2], high temperature [3,4], high densities [5,6], or in the presence of a heavy particle [7] (for an excellent review of these four mechanisms, see Ref.[8]).The basis for all these transitions is the level crossing phenomenon [9] which is usually illustrated by looking at adiabatic changes in the gauge field configuration and at the accompanying variation in the energy levels for the fermions resulting in a change in the fermion number. This description neglects the effect of the fermion back reaction: a change in the fermion density can introduce a change in the gauge field configuration, just as a change of gauge field configuration can change the fermion density. This is most easily seen in the Schwinger model where this back reaction of the fermions is responsible for oscillation in the fermion number [lo]. The fermion back reaction is a purely quantum mechanical effect being a direct consequence of the anomaly equation. Since the focus of fermion number violation has been in the study of solutions to the classical equation of motion (e.g., instantons and sphalerons), it is, therefore, not surprising that little attention has been paid to this back reaction. Further, it might be very difficult to properly take into account the fermion back reactign in realistic (3+ 1)-dimensional theories since the resolution of even seemingly straightforward related issues, such as the gauge invariance of the free energy at finite temperature and fermionic density [ l l ] , require a careful treatment of nonperturbative effects to be properly resolved [12].Fortunately, the situation is simpler in (1+1)-dimensional models where one can, through bosonization [13], take into account the fermion back reaction at the classical level. The present work illustrates some of the nontrivial effects of this fermion back reaction using a simple model which has been extensively studied in the past, namely, the Abelian Higgs model axially coupled to fermions (see for example [6,.'Electronic address: andre8gollum.phys.laurentian.ca 0556-2821/94/49(4)/1689(4)/$06.00 49The Lagrangian density describing this model is where D , = a , -i e A , and the space coordinate extends from -L to L. This model is to be regulated such that the gauged current ICn/py5$ is conserved while the vector current o...

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Gauge invariance and anomalous theories at finite fermionic density

Cited by 4 publications

References 22 publications

Vortex formation and dynamics in superfluid 3He and analogies in quantum field theory

Vortex formation and dynamics in superfluid 3He and analogies in quantum field theory

Sphaleron transition rate in the presence of dynamical fermions

Fermion back reaction and the sphaleron

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