OFFSET
0,5
COMMENTS
The rationals A(n) defined below appear in the expansion of the one-loop effective potential V1(y) for the thermal phi^4 model. See the Dolan-Jackiw, Kapusta and Quir/'os references. The expansion variable is y:=(m^2(phi))/(2*pi*k*T)^2 with Boltzmann's constant k, the (absolute) temperature T and m^2(phi):= m^2 + (lambda/2) phi^2 if the coupling constant is lambda/4! and the mass is m.
The relevant expansion of part of the thermal one-loop effective potential is ((pi^2)*((k*T)^4)/2)*sum(A(n)*Zeta(2*n+1)*(-1)^(n+1)*y^(n+2),n=1..infty) with the Riemann zeta function. The expansion parameter y is given above. See the W. Lang link for more details.
REFERENCES
J. I. Kapusta, Finite-temperature field theory, Cambridge University Press, 1989.
M. Quirós, Field theory at finite temperature and phase transitions, Helv. Phys. Acta 67 (1994) 451-583.
LINKS
Isabel Cação, Helmuth R. Malonek, Maria Irene Falcão, Graça Tomaz, Combinatorial Identities Associated with a Multidimensional Polynomial Sequence, J. Int. Seq., Vol. 21 (2018), Article 18.7.4.
L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys.Rev. D9,12 (1974) 3320-41.
Wolfdieter Lang, Rationals A(n) and more.
FORMULA
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Nov 10 2004
STATUS
approved