Perturbatively Defined Effective Classical Potential in Curved Space

Details Perturbatively Defined Effective Classical Potential in Curved Space Perturbatively Defined Effective Classical Potential in Curved Space

2003-01-16

arxiv.org/abs/quant-ph/0301081v1

Int.J.Mod.Phys. A18 (2003) 5521-5540

Physics

Quantum Physics

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all P

Scientific paper

10.1142/S0217751X03016471

The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -\beta V^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called effective classical potential containing the effects of all quantum fluctuations. The variable of integration is the temporal path average ${\bf x_0\equiv \beta ^{-1}\int_0^ \beta d\tau {\bf x}(\tau)$. We show how to generalize this concept to paths $q^\mu(\tau)$ in curved space with metric $g_{\mu \nu (q)$, and calculate perturbatively the high-temperature expansion of $V^{\rm eff cl(q_0)$. The requirement of independence under coordinate transformations $q^\mu(\tau)\to q'^\mu(\tau)$ introduces subtleties in the definition and treatment of the path average $q_0^\mu$, and covariance is achieved only with the help of a suitable Faddeev-Popov procedure.

Affiliated with

Also associated with

No associations

Rating

Perturbatively Defined Effective Classical Potential in Curved Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Perturbatively Defined Effective Classical Potential in Curved Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbatively Defined Effective Classical Potential in Curved Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-535316