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Interplay between Temperature, Magnetic Field and the Dynamical Fermion Masses

This research investigates the interplay between temperature, magnetic field, and the dynamical mass generation (DMG) for fermions in physics. The study explores the effects of temperature and magnetic fields on the fermion mass and the chiral condensate. Different approximations and analytic expressions are compared to understand the critical values for coupling, temperature, and magnetic field.

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Interplay between Temperature, Magnetic Field and the Dynamical Fermion Masses

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  1. Interplay between Temperature, Magnetic Field and the Dynamical Fermion Masses Enif Guadalupe Gutiérrez Guerrero Collaborators: Bashir, Raya, Sánchez Instituto de Física y MatemáticasUMSNH XII MexicanWorkshoponParticles and Fields2009Mazatlán, Sinaloa

  2. Contents • Introduction • DynamicalMassGeneration (DMG) forFermions at FiniteTemperature • DMG in UniformMagneticField • DMG in UniformMagneticField and at FiniteTemperature. • ChiralCondensate

  3. Introduction • DynamicalMassGeneration (DMG) forfermionsis a non perturbativephenomenonwhichcannotberealized in perturbationtheory. Ittakes place whentheinteractions are strong. • In thepresence of a magneticfield, DMG takes place forcouplingshoweversmall. Thispenomenoniscalledmagneticcatalysis. • Thepresence of temperature tries torestorechiralsymmetry. • Westudythemomentumdependentmassfunction in thepresence of oneorbothingredients and extractthefermionmass and chiralcondensate. Wealso compare ourresultswithearlierfindings.

  4. DMG at FiniteTemperature A. Ayala and A. Bashir, Phys. Rev. D67 076005 (2003). Workingwithbarevertex and explicity in theimaginary-time formulation of thermalfieldtheory

  5. DMG at FiniteTemperature After angular integration and keepingthelowestMatsubarafrequency, where D.J- Gross, R.D. Pisarski and L-G- Yaffe, Rev. Mod. Phys. 53 43 (1981). Analytic treatment implies that Tc =0.050533, in the Feynman Gauge.

  6. DMG at FiniteTemperature A. Ayala y A. Bashir, Phys. Rev. D67 076005 (2003).

  7. DMG in MagneticFields D.-S. Lee, C.N. Leung, Y.J. Ng, Phys. Rev. D55 6504 (1997). InvokingtheRitusmethod and workingwithbarevertex in theFeynman gauge where ForthelowestLandaulevel and in theconstantmassapproximation constants are of order 1.

  8. DMG in MagneticFields Beyondconstantmassapproximation. MagneticFieldfavorsthe DMG.

  9. DMG in MagneticFields Beyondconstantmassapproximation. Thereis no criticality in coupling.

  10. DMG in MagneticFields Beyondconstantmassapproximation. Thereis no criticality in eB.

  11. DMG in MagneticFields a=1.28521, b=1.13083 Comparingresultswiththose of Leung et. al.

  12. DMG in MagneticFields I. A. Shushpanov, A. V. Smilga, Phys. Lett. B402 351 (1997). D.-S. Lee, C.N. Leung , Y.J. Ng, Phys. Rev. D55 6504 (1997). when Thecondensate and the OPE.

  13. DMG at Finite T and Uniform B We work with the lowest Matsubara frequency and the lowest Landau level

  14. DMG at Finite T and Uniform B Miranskylikescaling a = 0.7982, b = 0.1139 a=- 0.7564, b= 1.3228, c= 1.0544,

  15. DMG at Finite T and Uniform B Thereiscriticalityforthemagneticfield

  16. DMG at Finite T and Uniform B Thereisalsocriticalityforthecoupling.

  17. DMG at Finite T and Uniform B eBfavorstheDMG buttemperaturedoesn’t

  18. DMG at Finite T and Uniform B a= .0505, c= 0.0066 Criticality curve

  19. ChiralCondensate H.D. Politzer, Nucl. Phys. B117 397 (1976) when Contrastingbothapproximations

  20. ChiralCondensate a= -0.4566, b= 0.0566 Thereiscriticalityforthemagneticfield

  21. ChiralCondensate eBfavorsthecondensatebuttemperaturedoesn’t.

  22. Conclusions DMG (T, B=0): • Wereviewthestudy of DMG in QED numerically. Weobtaincriticalvalueforthetemperature and couplingabovethisvaluesfermions can acquiredynamicalmass. Wechecktheanalyticalpredictions, and confirmthatthemassfunctionfalls as 1/p2 as p -> ∞. Moreover, weobtain new resultsforFeynman gauge. DMG (T=0,B) Wereview DMG and confirmthereis no criticalcouplingormagneticfieldintensity. Wegobeyondconstantmassapproximation. Wealsorealizethatthemassfunctionfalls as 1/p2 as p -> ∞. Wecheckourresultswiththeanalyticalexpresions.

  23. Conclusions DMG (T,B) • Westudy DMG withoutconstantmassapproximation and compare withearlierresults. Wework in thelowestLandaulevel and Matsubarafrequency. Weconfirmtheexistence of criticalvaluesforcoupling, temperature and magneticfield. Themassfunctionfalls as 1/p2for p -> ∞. CHIRAL CONDENSATE Theasympoticbehavior of themassfunctionguaranteesthatthecondensateisindependent of themomentum p whencalculatedthrough OPE. Wefindthatthechiralcondensateincreaseswiththecoupling and themagneticfield. However, thetemperaturetendstodestroyit.

  24. Chiralcondensate Usingthe trace of thepropagator, weobtainthesamebehaviorforthecondensate

  25. OPE

  26. MatsubaraFrecuencies

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