A non-perturbative path-integral based thermal cluster expansion approach for grand partition function of quantum systems

2002 ◽  
Vol 352 (1-2) ◽  
pp. 63-69 ◽  
Author(s):  
Sheikh Hannan Mandal ◽  
Rathindranath Ghosh ◽  
Goutam Sanyal ◽  
Debashis Mukherjee
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Cluster Expansion ◽  
Quantum Systems ◽  
Grand Partition Function

A non-perturbative cumulant expansion method for the grand partition function of quantum systems

2001 ◽  
Vol 335 (3-4) ◽  
pp. 281-288 ◽  
Author(s):  
Sheikh Hannan Mandal ◽  
Rathindranath Ghosh ◽  
Debashis Mukherjee
Keyword(s):  
Partition Function ◽  
Expansion Method ◽  
Quantum Systems ◽  
Grand Partition Function ◽  
Cumulant Expansion

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

scholarly journals Vacuum energy of a nonrelativistic string with nontrivial boundary condition

2018 ◽  
Vol 33 (16) ◽  
pp. 1850097 ◽  
Author(s):  
A. Jahan ◽  
S. Sukhasena
Keyword(s):  
Boundary Condition ◽  
Partition Function ◽  
Classical Solution ◽  
Path Integral ◽  
Integral Method ◽  
Vacuum Energy ◽  
Nonrelativistic Quantum ◽  
Relative Angle ◽  
Path Integral Method

We derive the partition function of a nonrelativistic quantum string whose ends are allowed to freely move along the two-angled straight solid rods. We first derive the classical solution of the model and then use it to derive the partition function utilizing the path integral method. We show that the vacuum energy is the sum of the Lüscher potential plus a term which depends on the relative angle between the rods.

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