Different symmetry realizations in relativistic coupled Bose systems at finite temperature and densities llaborators: R.L.S. Farias and R.O. Ramos Rodrigo Vartuli Department of Theoretical Physics, Department of Theoretical Physics, UERJ II Latin American Workshop on High Energy Phenomenology 5 th December 2007 São Miguel das Missões, RS, Brazil
Different symmetry realizations in relativistic coupled Bose systems at finite temperature and densities. Rodrigo Vartuli Department of Theoretical Physics, UERJ. II Latin American Workshop on High Energy Phenomenology 5 th December 2007 São Miguel das Missões, RS, Brazil. - PowerPoint PPT Presentation
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Different symmetry realizations in relativistic coupled Bose systems
at finite temperature and densities
Collaborators: R.L.S. Farias and R.O. Ramos
Rodrigo Vartuli
Department of Theoretical Physics,Department of Theoretical Physics, UERJII Latin American Workshop on
High Energy Phenomenology
5th December 2007São Miguel das Missões, RS,
Brazil
Outline• Motivation
• Study of symmetry breaking (SB) and symmetry restoration (SR)
• In multi-scalar field theories at finite T and are looking for the phenomena
• How a nonzero charge affects the phase structure of a multi-scalar field theory?
• Work in progress and future applications
1- Motivation1- MotivationThe larger is the temperature, the larger is the The larger is the temperature, the larger is the
symmetrysymmetrythe smaller is the temperature, the lesser is the the smaller is the temperature, the lesser is the
symmetry:symmetry:
Symmetry Breaking/Restoration in O(N) Scalar Models
Boundness:
+ unbroken
- broken0
Relativistic case:
The potential V( ) for –m2, N=1 (Z2)
Let´s heat it up!!
Thermal Mass at high-T and N
M ²(N=2)
For ALL single field models:
Higher order corrections do NOT alter this pattern !!
(1974)
O(N)xO(N) Relativistic Models
Boundness: λ>0 OR: λ<0!!
Thermal masses to one loop
Critical Temperatures at high-T and N=2
or i
M² (N=2)
Both m² < 0:SR in the ψ sector
SNR in the sector
Transition patterns
M ²
ISB
Transition patterns
Both m² > 0: sector:
unbroken sector : ISB
Temperature effects in multiscalar field models Temperature effects in multiscalar field models can change the symmetry aspects in unexpected ways:can change the symmetry aspects in unexpected ways:
e.g. in the O(N)xO(N) example, it shows the possibilities e.g. in the O(N)xO(N) example, it shows the possibilities of phenomena like inverse symmetry breaking (ISB)of phenomena like inverse symmetry breaking (ISB)
and symmetry nonrestoration (SNR)and symmetry nonrestoration (SNR)
But be careful:
Question: Can we trust perturbative methods Question: Can we trust perturbative methods at high temperatures ?at high temperatures ?
NO ! (but these phenomena appear too in nonperturbative
approaches) THEY ARE NOT DUE BROKEN OF PERTURBATION THEORY
~ O( T ) ~ O( T . T/m )
Perturbation theory breaks down for Perturbation theory breaks down for temperatures temperatures l T/m > 1
2 2
Requires nonperturbation methods: Requires nonperturbation methods: daisy and superdaisy resum, daisy and superdaisy resum,