Mass gap and vacuum energy of the Gross-Neveu model via the 2-point-particle-irreducible expansion

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 67, Issue 2, 2003, Pages

  Dudal, David ^a   Verschelde, Henri ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; CHIRALITY; ENERGY; MASS; MATHEMATICAL ANALYSIS; REDUCTION; RELIABILITY; TEMPERATURE DEPENDENCE; VACUUM;

EID: 0037438286     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.67.025011     Document Type: Article

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20. At 1 loop 2PPI order, there is no mass renormalization, hence (Formula presented) is the physical mass.
21. (Formula presented) is not defined since (Formula presented) We have (Formula presented)
22. (Formula presented)
23. We must add a source term, otherwise E cannot be treated as an effective potential in the usual sense.
24. Up to an irrelevant (integration) constant that can be dropped.
25. We notice that (Formula presented) (Formula presented) and (Formula presented) are the same for each MRS.
26. No (Formula presented) satisfying (Formula presented) was found.
27. Again, no solution for (Formula presented)
28. To be more precise, (Formula presented) and (Formula presented) The fact that the error grows fast between (Formula presented) and (Formula presented) and goes slowly to (Formula presented) for (Formula presented) makes us believe it is a rather lucky shot that the energy values are better for small N.
29. Also for (Formula presented) the error grows between (Formula presented) and (Formula presented) (Formula presented) (Formula presented), and drops slowly to 0 for (Formula presented)