Casimir pressure at two loops and soft boundaries at finite temperature

Luiz C. de Albuquerque

doi:10.1103/PhysRevD.55.7754

Access by Xinjiang University

Casimir pressure at two loops and soft boundaries at finite temperature

Luiz C. de Albuquerque

Instituto de Física, Universidade de São Paulo, P.O. Box 66318, 05389-970 São Paulo, SP, Brazil

PDF

Phys. Rev. D 55, 7754 – Published 15 June, 1997

DOI: https://doi.org/10.1103/PhysRevD.55.7754

Abstract

The first order Casimir pressure is computed in the $λ φ_{D}^{4}$ theory. Some peculiar results in odd space-times dimensions are noticed. Namely, the first-order pressure is beset by a divergence, proportional to the inverse of the distance between the plates. Hence, Dirichlet boundary conditions render the $λ φ_{3}^{4}$ theory nonrenormalizable at two loops. In order to understand this peculiar feature of odd dimensions we generalize a recent proposal to “soften” the hard Dirichlet walls. However, in its simplest form it does not solve the renormalization problem found in $D = 3$ .

References (15)

L. H. Ford, Proc. R. Soc. London A368, 305 (1979); G. Denardo and E. Spallucci, Nucl. Phys. B169, 514 (1980); A. Actor, Class. Quantum Grav. 7, 663 (1990).
D. J. Toms, Phys. Rev. D 21, 928 (1980); 21, 2805 (1980).
J. I. Kapusta, Finite Temperature Field Theory (Cambridge University Press, Cambridge, England, 1992).
G. Plunien, B. Muller, and W. Greiner, Phys. Rep. 134, 87 (1986).
K. Symanzik, Nucl. Phys. B190, 1 (1981); D. Deutsch and P. Candelas, Phys. Rev. D 20, 3063 (1979).
S. K. Blau, M. Visser, and A. Wipf, Nucl. Phys. B310, 163 (1988).
A. Blasi, R. Colina, and J. Sassarini, Int. J. Mod. Phys. A 9, 1677 (1994).
K. Milton, Phys. Rev. D 22, 1441 (1980); 22, 1444 (1980); C. M. Bender and P. Hays, 14, 2622 (1976).
A. A. Actor, Physica A 158, 38 (1989).
A. A. Actor and I. Bender, Phys. Rev. D 52, 3581 (1995).
N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1986).
C. Itzykson and J.-C. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1990).
J. Ambjorn and S. Wolfram, Ann. Phys. (N.Y.) 147, 1 (1983); E. Elizalde, J. Phys. A 22, 931 (1989); K. Kirsten, J. Math. Phys. (N.Y.) 35, 459 (1994).
R. Banach, J. Phys. A 13, L365 (1980).
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965).

[c1] L. H. Ford, Proc. R. Soc. London A368, 305 (1979); G. Denardo and E. Spallucci, Nucl. Phys. B169, 514 (1980); A. Actor, Class. Quantum Grav. 7, 663 (1990).

[c2] D. J. Toms, Phys. Rev. D 21, 928 (1980); 21, 2805 (1980).

[c3] J. I. Kapusta, Finite Temperature Field Theory (Cambridge University Press, Cambridge, England, 1992).

[c4] G. Plunien, B. Muller, and W. Greiner, Phys. Rep. 134, 87 (1986).

[c5] K. Symanzik, Nucl. Phys. B190, 1 (1981); D. Deutsch and P. Candelas, Phys. Rev. D 20, 3063 (1979).

[c6] S. K. Blau, M. Visser, and A. Wipf, Nucl. Phys. B310, 163 (1988).

[c7] A. Blasi, R. Colina, and J. Sassarini, Int. J. Mod. Phys. A 9, 1677 (1994).

[c8] K. Milton, Phys. Rev. D 22, 1441 (1980); 22, 1444 (1980); C. M. Bender and P. Hays, 14, 2622 (1976).

[c9] A. A. Actor, Physica A 158, 38 (1989).

[c10] A. A. Actor and I. Bender, Phys. Rev. D 52, 3581 (1995).

[c11] N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1986).

[c12] C. Itzykson and J.-C. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1990).

[c13] J. Ambjorn and S. Wolfram, Ann. Phys. (N.Y.) 147, 1 (1983); E. Elizalde, J. Phys. A 22, 931 (1989); K. Kirsten, J. Math. Phys. (N.Y.) 35, 459 (1994).

[c14] R. Banach, J. Phys. A 13, L365 (1980).

[c15] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965).

Physical Review D

Export citation

Export citation

Casimir pressure at two loops and soft boundaries at finite temperature

Abstract

References (15)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation